If the LED thing on the A-pilar is triangular with a button on it then you almost certainly have a Volvoguard 1 alarm as others have suggested. They were fitted to cars up to about 1995. Either factory or as a dealer option.
The Volvo fobs looked like the attached picture. They are quite rare now but crop up on eBay periodically.
There are several things that fail and cause people to abandon the system. Inside the fob is a 1MHz ceramic resonator which comes detached from the PCB. This results in the fob not working and the LED not illuminating. The fob can be easily opened and the component either re-soldered or replaced. Inside the triangular thing in the car is a small blue Murata variable capacitor which tunes the receiving circuit. This goes out of spec. Some have effected permanent repairs just by adjusting this capacitor. However, I found it had become unstable and wouldn’t stay in tune so I replaced it in my 1994 Wentworth. Relatively easy to do in situ if you’re a bit nifty with a soldering iron.
More detail on fob repair.
https://www.volvoforums.org.uk/showthread.php?t=253183
More detail on receiver repair.
https://www.volvoforums.org.uk/showthread.php?t=200312