dplusm1995

Just bought a 2006 Chevy Cobalt Coupe LS at auction for my sons first car. Got a really good deal but beating myself up that I didn't look at it a little deeper. The main two issues are:

Anytime you get up to 55mph, there is a violent shake that continues until you either go above 60 or back down below 55. The car had General Brand tires on them that were completely chopped up, so I put a new set of Uniroyal's on. It didn't fix the problem. I don't believe it's the alignment, as the car has no pull whatsoever. I took my hands off the wheel for a good 10 seconds and it took me straight as an arrow. Now, the guy that put the tires on did say that the back-passenger wheel looked as though it had been welded. (It has aluminum wheels) He said this could be the cause.

Also, there is something weird going on with the electrical.
1. Instrument Panel / displays are very hard to read. Dimmer switch does not work.
2. Drivers Side Door Switches: Driver auto window switch works 1 out of every 10 tries, passenger auto window switch works fine, lock/unlock does not work at all, and mirror adjustment does not work.
3. Passenger Side Door Switches: Automatic Window Switch will roll up, but not down. Lock/unlock switch will lock doors but not unlock.
4. Trunk pop will not work.
5. Radio display shows a few random letters/numbers but that's about it. You can change the stations and I believe a person could make sound adjustments if they knew the steps without having to read the display.
6. The RPM Instrument will "twitch" after the engine is cut off and the key removed. It will only last about 30 seconds once the key is removed.

We have checked fuses but didn't find any problems. Any chance these are just individual problems that need to be addressed or does this point to a bigger issue?