I have a GE Spectra. Oven wouldn't turn on, but when I turned on a burner oven would turn on for about 2 minutes then shut down whole stove. Burners come on for about 2 minutes too but do not heat up.

SOURCE: ge spectra xl44 stove

Most likely the oven ignitor is bad or weak.  You can look at it and see how it compares to the broil ignitor.  If you see a whitish color on the ignitor and if it doesn't fully glow then it needs to be replaced. 

SOURCE: GE Spectra range

All of the items you mention that do work, are 120 volt items.
All the items that do NOT work are 220 volt items.
Sounds like you have a voltage problem, you will need to use a meter to check if you have 220 volts a/c to the outlet the stove plugs into. Take care when doing the following, you will be around live voltage and could get hurt. If you are uncomfortable working with a live circuit best to call someone in to do it for you. Check for 220v at the outlet for the stove (where the stove plugs into), if you have it there, go to where the cord attaches to the stove and check at that point. You should have either a 3 or 4 wire cord on the stove, On the rear of the stove there is a terminal block that the cord is fastened to. Between RED and BLACK you should have 220v, between RED and WHITE and BLACK and WHITE you should see 120v. Another thing to check is that the nuts holding the wires from the cord to the terminal block on the stove are turned down tight. A loose connection there will give you the same problem you have as well.

SOURCE: GAS STOVE

yep replace the bottom ignightor take out the rackes remove the two bott screws in the oven remove the bottom plate and just keep going down

SOURCE: ge spectra gas stove top not lighting

If your top burners are not lighting or will not work, it is possible that the burners have become dirty or wet. Please follow the troubleshooting directions below before calling service:

1. Turn you burner to the Lite position:
   
   If you hear clicking or sparking, go to Step 2.
   
   If you do not, check your circuit breakers. If the circuit breaker is ok, we recommend that you schedule service by calling 1-800-432-2737 or schedule service online.
   
   
2. Clean the burner and electrode:
   
   First remove the burner grate, cap, and head. Use a needle or paper clip to poke through the holes on the burner head. Re-assemble and try the burner.
   
   Remove the burner grate, cap, and head. Even if it looks clean, wipe the tip of the electrode with a clean, dry paper towel and PRESS IT DOWN. Re-assemble and try the burner, again.
   
   Check to see if the burner works, If not, then go to Step 3.
   
   
3. Re-assemble - Make sure that each burner top matches its burner bottom. The burner top will lay flat if put on correctly.
   
   Check to see if the burner works, If not, then go to Step 4.
   
   
4. The spark igniter is operating properly, but the burner is still not lighting. At this point, we would recommend that you schedule service by calling 1-800-432-2737 or schedule service online.
   

SOURCE: GE spectra xl44 - Oven not working, broiler & stove-top burners fine

replace the ignitor for the oven. it's the lower one and not the one on top.