A team of explorers found a well preserved body of a humanoid alien in the Antarctic ice and managed to extract it for study purpose, there is no suspicious foreign object found beside the body. They bring the body to a lab to sequence the DNA and discovered that it is a silicon-based life-forms and another weird phenomenon is that there is no trace of any carbon elements or isotope inside the deceased alien. They are not sure if the ice that was covering the body forms around the time the alien died or after and they wanted to find out when did this alien died, is there any 21st century methodology available to solve this perplexing issue? answer with best accuracy wins!
Actually the ice it was found in could still tell them a lot. By aging the ice around the being, to begin, they will be able to identify a maximum age that it could be, or more accurately, the maximum length of time the alien was in the ice, in case it died earlier was preserved and finally laid to rest there...
Apparently Antarctica could have ice 1.5 million years old. But since this body is found and taken whole in the ice the expectation would be that it is much younger than that. To add, Carbon dating is only 'accurate' to a max of about 50,000 years. (up to 70,000 in special circumstances)
Considering the forces ice moving in a glacier has on stuff inside it, I would guess that for the alien to have survived intact (mostly) either it has a constitution of granite or it was left there within the 50,000 years.
Doing some more looking. The whole point of Radiometric dating comes from knowing how much you had to begin with. So any isotope you might try would be pointless since you have no idea how much of it might have existed in the sample (entity) in the first place.
So we are back to using the Ice dating that surrounded the creature for the best guess estimate.
Bowlturner mentioned dating the ice around it.
I'll expand on that with technology and artefacts associated with the body. Like a scene from Hogan's Inherit the Stars, maybe they will find his power supply used radioisotopes. Maybe parts of his field kit require small quantities of radioisotopes. Being technology and not happenstance abundance we can tell what isotope and concentration was meant in that application.
His artefacts will contain many materials and will be "simple" not living things (we suppose, for the story). Two materials in contact have stuck together due to random motion of atoms: we can figure out the rate at which that happens. Maybe the lubricant in a joint breaks down, slowly. The novel biological materials will be too hard to figure out anytime soon, but any simple materials found can be characterized, and several such measurements giving the same time scale is a good clue that it's right.
We might find that the lube breaks down, titanium from a part loses atoms into the lube, and lube works its way into the metal via diffusion, over scales on thousands or millions of years. Was his oil fresh when he died? We can assume essentially yes everything was fresh on that time scale. Even if his equipment was 50 years old we are talking about a million years of decay since then.
If the alien died recently (within the past few hundred years) and was on Earth long enough for its isotopic abundance to match that of the environment, you could try radiodating using silicon-32. However, the abundance of Si-32 isn't characterized well-enough to give you any sort of accuracy.
Other options exist, but they depend on the alien's biochemistry. For example, if it accumulates environmental uranium, you could try uranium-thorium dating: under ideal conditions, this is good out to a half-million years or so, long enough to cover any object found embedded in ice. Similarly, if it accumulates aluminum, you could try using the aluminum-26/magnesium-26 ratio for dating, with a similar range.