98 lumina, can’t shut off alarm

Hello all...

factory installed alarm on 98 lumina. 

History:  last year, remote would not shut off alarm...found battery ground cable loose and after tightening worked fine..for awhile.  Six months ago (car is used only short distances every few days) car battery would die if not used for 4-5 days.  Would trickle-charge and would be okay unless left 4-5 days without using.  Got more frequent and just figured battery was old, so replaced with Die-hard (afterwards, heard they were crappy).  Car still died if left to sit 4-5 days, so took to mechanic who said current draw was too high when car not being used (think he said half an amp higher than acceptable) and that would drain battery...his verdict: take out one of 60 amp fuses so draw is less (that sounded like a cheesy way of fixing, but he didn't charge me anything,) so i removed it and it has been ok, but I have been using car more regularly lately, so i don't really know.

OK, problem is yesterday I used the car and made three or four stops, and each time i restarted the car there was no indication of battery discharge...started right up strongly.  But when I got home and went to go out about an hour later my alarm remote would not beep and turn off the alarm, or let me start the car (only difference was it was now lightly raining out).  The alarm went off as I opened the hood to check the ground cable again...but it's tight. Put the battery on trickle charge, but it seems all charged and not drained, yet the remote still won't work and I can't start the car.  Got the spare set of keys and tried the remote, that didn't work either.

Can anybody help this car-dumb guy with this problem?  Thanks much for any consideration!