I have a '89 Corsica with a 2.8. I drove it and it ran fine. Ten minutes later when I went to use it again, it began running very rough, whole car shook, and it now has little power, as seen by the fact that it will barely go from 0 to 35 in four blocks. Any suggestions as to what could be causing this? My dad says it is acting like the timing is off, but there is no distributor.

 

Is your engine light on? If so under the dash just to the right or left of the steering colum you have a plug/connector with nothing hooked to it. It may have a cover on it. It will be a 12 pin connecter. If you jump the top 2 on the right side, then turn the key on the light should flash once, long pause, twice short pause. That is a code 12, that means you are into the diagnostics, it will flash that 3 times, any code after is what is wrong. If you call Auto-Zone or Advance Auto Parts they should be able to tell you what the code means.
As for the timing you dad could be right. You may not have a distributor but you do have a timing chain. The distributor is turned to adjust the fire on the sprak plugs. The timing chain is used to adjust the cam shaft to the crankshaft so the valves open at the proper time. I don't know about Corsicas but I do know that GM used a metal gear with plastic/nylon teeth on the cam gear. Once they wear out as they are prone to the chain can jump easily and your timing is off.
If your light is on check that first.

 

try cheaking to see if all the plug wires are on tight. see if that helps.

 

Change the fuel filter first. Cheap to do, and can't go wrong. Sounds like that is what it is...