Any guesses as to what could be wrong?

not sure about your particular car, however my mother had a honda civic when I was younger that would do the same thing......her problem was actually the injectors were fouled out from her sister running the car completely empty on gas which in turn broke the fuel pump and fouled the injectors.........I would go to a local parts store ie: auto zone, o'rileys or napa and see if you can use the computer diagnostic tester.....it plugs in under your dash and will give you a readout of a combination of blinking lights or alphanumeric code which the store should have a book to decode it and tell you exactly whats wrong, usually you can use the handheld cpu for free? good luck