Probably, but you likely wouldn't drive it away.
Not only will the batteries be completely discharged, but the rovers have gone through a large number of lunar days since then, creating a large thermal cycle. The number of thermal cycles is on the order of 500 for each one, and the cycles are brutal, going from -150C to as high as 120C each time. Even averaging that out a bit, that's still a 200 degree thermal swing, which will cause problems will all sorts of things.
The wheels are composed of a variety of metals. Most metals have a slightly different expansion coefficient, most likely causing them to have expanded/contracted at different rates. No doubt they have some holes in them by now, the best bet would be to just replace them. Similarly, the seats are probably gone. The metal frame is probably mostly intact, but will contain some cracks in it, causing significant losses of structural capacity. No doubt there would be other problems as well. The exact types of problems are difficult to guess ahead of time, but it would require bringing a whole lot of spare parts, for technology from 40 years ago. I'm also not sure, but I would suspect that some of the items, such as the tires, have actually exploded, resulting in some sort of collateral damage to the rover.
In addition to the thermal cycles, there are effects caused by the moon itself. While there isn't much of an atmosphere, the dust slowly flies across the moon, meaning that dust most likely covered it. Most likely, there are a few small impacts as well from micrometeorites. And the electronics are probably fried completely as a result of being exposed to high levels of radiation for years. The bearings have probably seized in the wheels, and overall, they are probably in really poor shape.
From the images taken of the LRVs from orbit, it appears that they haven't completely fallen apart, but they are darker than I would expect them to be. I can't see the antenna mounted on the rover as is seen in the photograph above. In fact, the rover itself isn't visible, only the shadow. This indicates to me that it is either covered in dust, or most of the interior stuff has fallen off.
My personal thought, if you can get to the rovers, take them back to Earth to put in a museum. Making one of the lunar rovers work would be more akin to restoring a classic car that hasn't been taken care of at all for years, it would require a lot of time and energy. It seems more suited for a museum. This should fall under similar rules to the Apollo Engines found on the Ocean Bed, NASA wants some say, but the person who finds them has a lot to say about what happens.
Just to give you an idea of how well something can survive on the Moon, the Surveyor 3 lander was visited by Apollo 12. Some of the Surveyor landers survived multiple lunar nights, but Surveyor 3 failed to accomplish this task. There is actually an entire paper written on the subject. The results are that everything survived relatively well for the 2 years Surveyor was on the Moon. There was a failure in one of the legs, discoloration, dust contamination, and failure of the electronics, but otherwise the spacecraft appears to be in good overall condition.
Thus, I suggest just bringing your own rover. It'll just work better that way. The lunar rovers weren't all that difficult to get to the moon 40 years ago, it shouldn't be all that difficult to make a better replacement for them.