I have a 2008 Subaru Impreza standard with 139,000 miles on it. I just recently replaced the AC Compressor and the next day the car would not start and was completely dead, no dash lights or anything. My first thought was to jumpstart it, which worked and I let it run for about 10-15 minutes, and then it died. I attempted to start it again and nothing happened, still no dash lights. I also attempted to jumpstart it again and nothing happened. I figured it might be a battery problem so I bought a new battery and put it in. When I turned the key, all the dash lights came on but the engine would not start, not even crank or click. Also, the old AC Compressor did not have a belt on, so I'm wondering if now that it has a belt if it could be messing up something else. Just a thought. Hope somebody can help me, thanks.
The belt which drives the AC compressor on the Subaru engine does nothing else; it goes around the crankshaft pulley, to the compressor, and then past an idler pulley which handles the tension. If that belt was not present, the only effect is to prevent the AC from working. If the belt was too tight, the crankshaft pulley would still turn, so you don't have any issues there.
I think the issue is the alternator. To replace the AC compressor on a Subaru engine, you need to disconnect the alternator cables which run across the top of the compressor. Check that these have been reconnected correctly. There is a red one which bolts to the top of the alternator, and a plug which clips into the side. In the past I've had the alternator bolt shear off and the plugs disintegrate (I work on old Subarus a lot..). Do NOT accidentally short the red connection to earth - it's always live, even if the engine is turned off. You should disconnect the battery if you ever work on or near the alternator.
Try another jump start - there's no guarantee that the new battery has a full charge. After that, I'd be checking the alternator; if there are no bad connections, it may be on the way out.