I recently upgraded to a T2i from the original Digital Rebel. I usually used the Canon EF 35-105 lens on the old Rebel. When I put that lens on the T2i after about 5 seconds everything goes off on the camera. Turning off/on the camera doesn't help, I need to switch lens and re-insert the battery to get it to work. The other lens I have from the old Rebel are a Canon EF 50mm 1:1.8 II and Canon EF 75-300mm 1:4-5.6 III they both work fine. Is that lens not compatible? Seems kinda weird to me.
Yes it's compatible, being an EF lens. But as jrista states is a very old lens. It may have malfunctioned, or more likely need it electrical contacts cleaning. The little gold bits at the back that allow the lens to talk to the camera get dirty over time and no longer conduct a good electrical signal.
Soft pencil erasers are recommended for light cleaning, failing that any alcohol based cleaning fluid suitable for electronics should do the trick.
Or use this as an excuse to get a new lens :)
The EF 35-105 is one of the oldest Canon EF-mount lenses, and if I can remember what I've read about it, it sports a pretty old AF mechanism. It may indeed be that the AF mechanism isn't compatible with newer cameras, although generally speaking, any EF lens should work with an EF body.
Something else you might want to consider is the lenses resolving power. The T2i has a very high resolution 18mp sensor that has some very small photosites. Comparing the MTF chart of the EF 35-105mm to the MTF chart of the EF 24-105mm, the older lens tops out at 0.9 at best, and falls to around 0.4 as it is stopped down. The 24-105mm remains nearly perfect for most apertures, and stays above 0.6 at the tightest apertures throughout most of its zoom range. The 24-105 will offer considerably greater resolving power with a very high resolution sensor, where as the older 35-105 may not offer enough resolving power at anything other than its ideal aperture to really get the full benefit of the T2i's 18mp sensor.
Given that you are having trouble with the 35-105, it might be time to sell it, and trade up to the much improved 24-105 L if you need something in that range.
Just FYI I have the vintage Canon 35-105 and it works perfectly with my Rebel T1i - very sharp.
Here is just an extra piece of information for you. I found this site very useful when I first started getting into the world of Canon DSLRs.