Ok, I just tried that. Renamed the folder and changed it back. Unfortunately no change to the problem.
I just talked to my host's support and we tried a few things. They were able to deactivate individual plug ins for me by changing the plug in name and then changing it back. That basically "broke" the plug in and started it again. But I still can't manually deactivate that same plug in through WP. So even turning it off and on at the back end as you suggested didn't solve the problem.
I also noticed that when I try to activate or deactivate a plug in, I get the yellow box at the top of the page that says Plug In Activated (or deactivated). So WP seems to THINK it is doing something. But when I look at the plug ins themselves, there is no actual change.
I also tried deleting active plugs in by clicking the box and choosing delete from the drop down. That also didn't work. So basically anything I try doing manually won't work.
FWIW, the plug in that wouldn't install was WP to Twitter version 2.5.9. I finally just deleted it (which worked b/c it was never "active"). But still none of my other plug ins will work, which presumably they would if that was what had caused the problem. This was the most recent plug in i tried to install and everything was working before then. So either that caused some sort of permanent problem, or something else is going on with wordpress.
Any other suggestions? All my other plugins have been working fine until now when none of them seem to work.