Part One - Assuming the events of half life have not yet occurred; that the facility was abandoned before the game's events....
Most (but not all) of the base structure would still be intact. For sake of real-world comparison, I'll have you look at this abandoned nuclear missile silo (which is currently for sale for $4.2M if you really want it). [As an aside, I think it's hilarious it's listed as a "Potential Hemp Farm" lol]
Many of the structures, ramps, catwalks, etc are all similar to what you see in the Half Life game (or rather vice versa - the developers apparently did their research!). Although this facility was built in the 1960s, the structural integrity is about that of what I would expect from the 1990s. Also, these things take a long time to build, so even if it had 1990s era computers in it, the structure would have begun earlier. From what I can find, this is about what you would expect.
Fast forward not sixty years but five hundred... what would it be like? Take a look at this house built to last 500 years. Notice anything? The main supports are all similar to the main supports in the silo, just with padded with concrete (to prevent temperature and water differences). Unlike this house however, the Black Mesa facility is underground - just like the silo. The control for temperature is much better, but water is a significant issue underground. Depending on where the water table is, water leaking through the concrete after five hundred years could get onto structural beams and start to rust them. What's interesting in the silo pictures is that the structural beams for the catwalks are mostly steel beams (some of which show some rust already), but the main structure of the rooms themselves are concrete, and the beams close to them are either in concrete or thickly covered in some type of water-resistant and temperature-resistant material (I've been told this is a multi-layer substance with kevlar at one point, but don't ask me how I know that.... friend of a friend).
So we can safely say the rooms would still be there. The catwalks would be iffy at best. This might vary room to room.
For electricity - those generators are gone after 500 years. The oil would rust the components. So no luck there. Surprisingly some computers might still work, but again, very hit or miss. This is also assuming they were turned off before the facility was abandoned. Things like water pipes and sewage systems would be flawed or compromised, but parts could be salvaged.
Now all this does not include the possibility of pests or diseases working their way it. If that is the case, the facility would be deeply compromised and highly unstable. Given the depth underground of the Black Mesa facility and it's controls in place, I doubt pests would be that problematic, but it's worth mentioning.
Overall... a major overhaul would be necessary, but the main structure would be in tact.
Part Two - After the Half Life event
Best case: radiated wasteland with few live forms left. You can read about radioactivity in Nevada after fifty years. You can also do research into the Waste Isolation Pilot Plant in New Mexico which handles a lot of nuclear waste. The details of containment is important here. If the core structure is compromised, the whole area becomes a radiated wasteland. That's part of why that location in New Mexico was chosen for WIPP; in a worst-case scenario that area is already one of the most arid and isolated in America, so the damage would be minimal to surrounding life.
Similarly for Black Mesa, after a tragedy compromising core structural integrity, all the nuclear and radiation stuff would leak out. Hence Gordon's hazmat suit. Water would get in everywhere, compromising structural beams, and after five hundred years most rooms would either collapse or be unstable. Forget about catwalks. Pests everywhere. Well, either radiated pests everywhere or nowhere because there would be no life.
As a location it would have little value except as an archaeological dig site, or perhaps scraping metal. The radiation would still be everywhere, keeping life unstable and unlivable.