Why did the engine gag on acceleration, then backfired a bunch & now won't start?

I have a 1992 Subaru Loyale with 308K (80K on a rebuilt engine) and a few days ago I power washed the engine and cleaned the K&N air filter and drove it home with no problems. At home I changed the fuel filter and just before I started it up I wiggled the distributor cap and spark plug wires to make sure they were secure. Then the car started up as normal.

But as I pulled on the throttle cable the engine started to gasp. If I reved the engine up slowly the RPM will go way up and it sounded normal. But there is no power from the engine to actually drive the car. The car idled well for a while and then started less often. Then it wouldn't start at all and was backfiring too.

There was no check engine light on when the car was barely running. Sometimes in the past I had an intermittment idle problem where the check engine light would come on and the car would rev up and lose power and rev up again. If I just started driving or turned the car off and restarted this problem would go away.

So far to get the car running again I've changed the cap and rotor, plugs and wires, put in a new battery, checked all the fuses, made sure the spark plugs are getting a spark and checked the timing belts to make sure they are still in position.

I even put the old fuel filter back on since write after I replaced it was when all the problems started.

I replaced the fuel pump back in 2008 only to find out it was a bad pump relay wich I replaced with one I got from the junk yard. I still need to do a compression test. When I turned the engine over it doesn't sound so smooth and every four cycles or so hits a rough spot where the starter sounds strained. Still sounds of backfiring but not ignition backfiring.

Any idea what might be wrong? A mechanic is saying it might be the mass air flow sensor but I don't know how to test that other than to examine it and make sure it's clean, which it is.

Thoughts?