Car Problems Celica seems like its going to die when acclerating ?

you should be able to get that check engine light inspected and reset for free at any local parts store. as for the electrical issue at certain rpm's, i wouldn't suspect the battery on that one, as there is no direct link between the battery and engine rpm. even if your battery is bad, your alternator should be providing the power as long as the engine is running. i would suggest you take your alternator to a parts store and have it tested. a code for low charge would indicate the alternator as well, so have the computer scanned before you yank out the alternator. make sure you specify that the problem only occurs at certain rpm's so they can spin the pulley faster if they need to.

Get a free scan performed to start with so you know whats what and if you know the battery is weak buy yourself a Interstate battery with 850 cold cranking amps.