Let's say there is another planet in our solar system that harbours sentient life and this sentient life can build castles, buildings, and other such structures.
When would we notice that?
We can see the planet but we can't see lifeforms through basic telescopes - they're not close enough.
They don't have technology to send signals - we end up finding them.
The Great Wall of China can be seen from space!
Not quoting you, obviously, but it's a thing we've all heard a lot. We can see a load of things from space - with Google Earth I can see my house! It's good that you don't seem to be making that mistake, but on the off chance that was in your head, I just wanted to make sure we're on the same page.
I was a bit confused by your question though:
We can see the planet but we can't see them trough basic telescopes
I'll do my best to answer your question anyway.
I'd like to direct your attention to Mars. According to the link I've attached, many famous observers tried to learn about Mars with a standard advanced telescope of their time. They learned about how certain parts of Mars's orbit took it further away then it should've been, indicating some knowledge of a non-circular orbit and one that is not synchronous with Earth's orbit. They also started noticing Mars's polar ice caps expanding and contracting. Later on, they started noticing the massive dust storms we know Mars for (although they didn't know that that was what it was). If this is the tech your people have, they'll probably only notice this much. All of these observations took place by early 1800s.
By the mid-1800s, people were noticing features on Mars itself. People started making maps of the surface by this time. Not all of it was accurate, but what was very accurate was the rotation of Mars (which we figured out to be accurate within a tenth of a second). By the early 1900s we had maps of canals on Mars (we were taking photographs at this point), but later on we noticed other features, but almost a clear absence of canals.
Just by this level of tech, we can safely assume that without putting something much closer to Mars (like a satellite) we can't be too sure of buildings built by an alien race unless it's really obvious and changes the planet itself. Now, however, we can take pretty great images of Mars from Earth (no need for satellites), but our optical and digital zoom technology had to be refined a lot, and our best images are taken from out of our atmosphere to prevent distortion. Also, one reason we have such nice pics of Mars is because it has barely an atmosphere, so nothing to get in our way when we're looking at it from outside.
To look at your question again: you can't see this planet with a telescope, but you know it's there. Mars in our real world case could be spotted with the naked eye and observed with a good, old-school telescope. We still can't see anything on Mars though - until some nice pass-bys with various probes and satellites around Mars. That's despite having an advantage over your case. With your logic, the planet would need to blow up or something so we can notice it. I'll correct this answer if that's not what you meant.
EDIT: From comments and from clarification from the asker, I'd like amend my answer. Unless the structure the aliens were making on this planet were big enough to be noticed like dust storms, polar ice-cap expansion/contraction, or some other massive weather phenomenon, the odds of your people sitting on another planet being able to notice them is pretty slim. So, if they build a bunch of Empire State Buildings - no one would know. Now, if they had fast-growing cities or other megastructures under construction, they could be noticed, given that these construction projects weren't mistaken for weather activity.
It would depend on the distance to the planet, the composition of its atmosphere, their technology level, and our own.
Translated to our solar system, if they were on Venus we'd never know about them until we visited the planet because its cloud cover makes seeing much of anything on the surface impossible with visual instruments. On Mars, a large enough structure (say a few dozen to hundreds of kilometers across) might be visible from earth with a powerful enough instrument.
On Titan, forget about seeing anything, the optical resolution of your instruments will not be enough to see things much smaller than the size of Titan itself.
But even on Mars, you're looking at MASSIVE structures. Say something the size of a major mountain. And how'd you determine it was artificial? We've long thought the "face on Mars" was artificial, until a probe in orbit around Mars got images of high enough resolution to see that it wasn't.
Continuing on from cyber101's good answer, studying the early history of sending probes to Mars is probably a reasonable place to start and then add a dose of speculation to cope with your scenario.
Despite studying Mars through telescopes for many years, it wasn't until the Mariner 4 probe in 1965 that we got images from Mars good enough to resolve large craters. That was from a range of less than 10,000 km using a slow-scan video camera attached to a telescope. A couple of things came out of that: the surprise that there were visible craters; and the acknowledgement (by Carl Sagan and others) that the 22 images obtained was not really enough to "conclude there was no intelligent life on Mars".
However, as our probes get better, and once the alien civilisation gets advanced enough to build many large cities, starts transmitting radio or other electromagnetic waves into space, or starts to radically alter the landscape with the kind of infrastructure associated with a civilisation - farms, roads, airports, docks, artificial lights, that kind of thing - the signs of intelligent life become harder to miss, even from far away.
Even now, though we are sure there is no intelligent life on Mars, the question of whether there ever was any life on Mars is still an open one.
Depending on how you define it, one of the larger structures humans build is a city. The built-up area of Beijing has an area over 4000 square km. The lunar crater Aristoteles has a diameter of 87 km, so an area about 6000 square km. So Beijing ought to be visible from another planet with a good telescope. Possibly by way of the concentric ring-roads, of which it has seven. When people paint a giant target on their planet, possibly somebody should look.
For viewing of Earth from Mars, the Earth would show its night side quite frequently. City lights might be the first things visible. Viewing from a planet closer to the sun would mean it's hard to see the night side of the planet.
For individual artifacts, possibly airports would be a give-away. The longest runways are several miles. A structure this long, and this straight, is a strong hint that somebody is getting up to something artificial.
As others have said, that depends on the planet's distance to us and its atmosphere.
For thick atmospheres, such as Venus and Titan, we will know they are there when we either:
The latter will only work if the other planet is closer to the Sun than we are. The point being that there will be no visual confirmation in those cases.
For atmospheres like Mars', by around the 1800's. Back then astronomers such as Giovanni Schiaparelli saw what they thought to be canals on Mars. Those were not canals. But if there is a civilization in another planet, they will have an impact on that world's forests (or equivalents), which would be measurable throughout time. Mars is not geologically active, so any fast changes on its surface would most probably be driven by bioological activity. Whether that activity is intelligent or not would take more time to assess. If they could have radio as we do, we would start communicating around the time both planets have it. Since the question forbids that, we will get visual confirmation by the 60's, when the first interplanetary probes are launched (Mariner 4 arrived on Mars in 1965).
