How do i disengage the alarn on a 1996 jeep cherokee

double posted, backup on post. see answer.
a classic question.
RTM

Ground the purple and yellow wire under the dash on the passenger side. This should fix your security issues.
If the alarm is sounding, unlock the driver door with the key.

inspect the cable sounds like you broke it

At the base of the arm where it attaches to the drive stub, you should see a "L" tab made of stainless steel. that tab swings out, disengaging the arm. you then need to pull and wiggle the arm a bit to get it free from the stub. When you put it back on, make sure you swing the tab back in or the arm will fall off later.

Disengage the 4wd.

disconnecting it may cause more problems!!
have you had your battery checked??
if the battery voltage drops too low while just sitting there, it will sometimes cause the alarm to go off!!!

If the jeep is all wheel drive, it's 4wd all the time with some slippage done through the transfer case.

I need the bulb for the roof light for the 1996 Cherokee

There has to be a bleeder there unless someone broke it off. If so, your best option is to replace it. In order to be malfunctioning, there has to be a reason. Air just does not enter the system by itself... Either the clutch master, slave cyl or a line between the two is bad, or the clutch itself is worn. Check everything carefully before deciding upon a repair plan.

try to get yourself haynes repair manual book no: 50010

covers the jeep cherokee in great detail