Welcome to the forums!
Sorry to hear about the problems you're experiencing with your Corolla. The orange light that illuminates on your instrument cluster will be the check engine light (CEL). Fortunately you can easily diagnose the problem(s) by using a stretched out paper clip. Simply pop the hood, locate the OBD-I diagnostic connector (a small black box most likely next to the left strut tower), open the lid and put one end of the paper clip into the port labelled E1, and the other end of the paper clip into the port labelled TE1 (the labels are found on the underside of the cover, much like a fusebox).
Once that's done, sit in the driver's seat and turn the ignition to the 'ON' position (but
don't start the car). If your connections are secure then the check engine light should start flashing. Take note of how many times the light flashes as this is the diagnostic code it is giving you. For example, code 12 would be shown as one 0.5 second flash, a 1.5 second pause and two 0.5 second flashes. If more than one code is in the ECU's memory, then the codes will be grouped in numerical order, starting from the lowest number with each code separated by a 2.5 second pause. If you have no codes, the check engine light will flash continuously at 0.26 second intervals. If your check engine light fails to illuminate at all however, then check that your paper clip connections are secure. Sometimes it takes a little bit of wiggling to get a decent connection as there's grease in the holes (make sure you don't remove any of this grease).
Once you've got the code, head on over to the
Older Generation Corolla forum and do a search. If you don't manage to find anything useful, feel free to start your own thread. Let me know if any codes come up and I'll tell you what it means.
Good luck, and once again, welcome to Toyota Nation!