Was the antenna mounted on the top left corner of the windshield?

I'm thinking it to be an antenna problem.

The way I see it as is that when they replaced your windshield, they had to pry off the antenna which is stuck on the windshield with a double sided adhesive. They might have had problems pulling the antenna off and possibly opened the case of the antenna itself and damaged some of the internal components of the antenna.

I'd try going to a local car audio shop that sells the same brand alarm you have and try to test out one of their antennas from their products and see if it works.

Or take it back to the place you had it installed and say you think your antenna is bad and ask them to test it by replacing it real quick and seeing if the new one works. All while neglecting to tell them that you had your window replaced

Edit: Just saw you had it installed for 3 years. Try to find an autopage dealer around and see if their nice enough to let you borrow an antenna to test if you have a bad antenna. Should try to give the place you got it installed a shot as well, they usually offer lifetime warranties on installs, but with this being a potential bad antenna problem, I'm not so sure. Worth a shot though.