my car: 95 accord ex, 2.2L vtec, sedan, manual tranny

for months now, the car would intermittently not start. doesn't matter if it's cold or warm. i hear just one click when i turn the ignition on. i figured the starter is on its way out. but then it got weird...

one day i was able to start the car with no problems but the engine didn't sound right...higher pitch than usual. i didnt pay much attention to it coz i figured it just needed some time to warm up. but then the radiator fan would go on and off for every couple of seconds...and in sync with the ABS light on my dash also going on and off every couple of secs. of course, this got me worried so i immediately turned off the ignition and pulled the key out....but the engine was still cranking slowly for at least 5 seconds without the key in the ignition!

can someone pls enlighten me with what could be happening?