Identify This Alarm Remote, Ignition Disabled

First post. I know NOTHING about car security. Bought a used Subaru Forester 5 years ago that has an aftermarket alarm that I don't use. I might be describing this wrong, but it's my understanding that the alarm has some kind of ignition disable function? For example - my battery died earlier this year, and after putting in a new battery and trying to start the car, there was no sound whatsoever, as if there wasn't even a battery in the car. I had no idea what was going on and had a mechanic look at it. He noticed the aftermarket alarm and asked if I had a remote. I looked through the stuff I got with the car from the prior owner and did find a remote. Put a new battery in it and gave it to the mechanic, and he was able to reset the system and the car started (I wasn't there when he did this). I unhooked the battery this weekend, completely forgetting about this ignition disable thing, and now I'm in the same spot. I don't want to get the car towed to the mechanic again and would like to reset the system myself, but I don't know how to do it. I don't know what brand the alarm is. There's no markings on the remote. I've looked at pages and pages of images on Google and can't find anything that looks like it. I'm attaching a pic of the remote and the receiver that's mounted near the fuse box (there's a button on it as well). Can anyone help me out?

Sorry. Topic title should read: identify this alarm remote (ignition disabled) 2006 Subaru Forester. Regular key. BASIC car. A 4 button remote and I feel like a caveman.

I wouldn't know what brand alarm system that is. However, I do have a recommendation. Check the wires in the ignition harness for a wire that has been cut and spliced into the alarm. It might be white/blue. Cut it away from the alarm and put it back together. See if that solves your starting issue.My ex once told me I have a perfect face for radio.

Disconnect the battery. Turn the key to the On position. Connect the battery with the key on.

Thank you! I got it started Monday night by doing as you suggested. Upon reconnecting the battery the interior lights came back on and the clicking below the dash stopped on its own without me having to play with the remote. Everything looked normal, in other words. However, it did not start initially. I got complete silence when I turned the key. I took the remote and pressed lock and then unlock, tried again, and it cranked. Maybe I only needed to press one or the other? I have no idea, but I got it started. I'm now carrying the wrench I need to disconnect the battery if this ever happens again. Thanks again.