Can't turn alarm off!

I have a 1990 Oldsmobile 88.
I went to start it and got nothing, it didn't turn over or click, just dead, except the alarm (which I didn't know I had)started going off. We couldn't turn it off and finally cut the wires to stop the noise.
With a new battery I can finally get the car started although it's stubborn, but as soon as I hook the battery up the alarm starts up again and drains the battery.
I tried removing each of the fuses, to cut the power to the alarm, but it continued thru each fuse.
Any ideas on how to turn off the alarm?
Any help would be greatly appreciated!
Thanks

 

Is this alarm an aftermarket one? Though, I don't think these cars came from the factory with one, my 92 don't have one.

 

I don't have any idea! I bought it used without a manual. I would have to guess that it didn't come from the factory. But I can't be sure. Does that help find a solution or just make it worse?

 

OK. Remove the lower insulator panel under the dash on the driver's side. Look up in there and see if you can see a black box about 4x4" and about 1" thick, with a bunch of wires coming out of it. If you see one, that would be the alarm module. You will need to trace where the wires go and remove them where they are spliced in, then tape up any bare wires that are part of the vehicle's original harness. Then remove the module. Or, I guess you could just remove the power and ground wires from the module and leave everything else where it is to save some time and trouble.