1999 Acura Integra Car will only jump and sometimes shut o

Thank you so much for your help- I just pushed this car 2 miles down the road because it died and am freaking out because I have no idea where to turn next! THank you so much for your help- it is greatly appreciated! My boyfriend just bought this car- everything was running perfectly at first. It was a show car- with lexus front end conversion w/ 10k halogens, 2 12" subs, and suspension airbags. The car started to not turn on, sometimes would, the rest of the time would have to be jumped. For a couple days, it would run fine after it was jumped. Then one day it just died in the middle of the highway while going 65mph. We bought a new Optima battery, thinking the accessories were taking up too much power, but it only worked for 2 turn ons, each time driving for only about 10 minutes, then went back to not starting. We then replaced the alternator, recharged the battery at autozone, and it ran beautifully again. Thought we fixed the problem, but after turning it on the second time, after 10 minutes of driving, it started losing power again. The next time we tried to turn it on, it wouldn't- but atleast would make a spark. I unplugged the cable of the system/ airbags from the battery and have left it unplugged for about a day. Now, it can be jumped always, and we took it 100 feet down the road when it began shuttering, losing power, not shifting into gear, and eventually dying. I thought it was wiring with the system(which still might be a problem), but then why would the car still die when that cable is unplugged? My friends who used to work on cars installed the alternator- could it be badly connected? I have had people mention to get a capacitor for the sytem, change parts in the ICM, but I am running out of money here and can't afford to replace everything just to figure this out.