Powering sub with 4 ch amp?

[J Rod]

So I had an old 10+ year old amp and sub lying around that I was hoping to hook up to my existing BA stereo. I bought an X3RCA adapter and hooked everything up, it worked but I kept getting a constant thumping heartbeat sound from the sub even with the stereo turned off. I went over all of the wiring and everything looked good so I decided to try out a different 600w 4 channel amp that I had. I bridged the 2 rear channels to the sub and it worked perfect! So I finished mounting the amp and sub and tested it out one last time, no issues. Then about a week later I drove the car to work and noticed there was no bass. I popped the trunk at work and sure enough, the sub wasn’t hitting at all even though I did have power to the amp. Now I’m wondering if I blew the sub. It’s honestly so old that I don’t even know what the specs are on it. I snagged a brand new 250w RMS Single Coil 4 ohm Kenwood sub for $30 that I’m going to replace my old one with, but before I do that I figured I’d make sure I don’t have the amp hooked up wrong so it doesn’t blow this one too. I only know enough about this stuff to be dangerous so hopefully you guys can help. I’ve never used a 4 channel amp to power a sub before, is it ok to have those 2 rear channels bridged (300wx1 @ 4 ohms) to a 250w sub? Also, is there an issue with me leaving the front 2 channels unused? I do intend to use them eventually to power my front door speakers. TIA