Do some basic troubleshooting first. All you know right now is that your fuel pump is turning on.
First pull the plugs and check them for anything obvious.
I'd go ahead and just replace the fuel filter. They are only a few bucks and easy to replace.
Since you can start it sometimes, but it runs rough, get it started and pull one plug wire at a time. It should get worse when you pull off a wire. If it stays the same when you pull one of them, you most likely have some ignition problem with that cylinder. If the plug, wire, and ig module check out, you could possibly have a stuck valve, rocker, pushrod, etc. and you can check that by just checking the compression with your finger over the plug hole (be sure and disconnect the pcm fuse first, so the car doesn't start).
If that doesn't give you any info, buy a can of carb cleaner, and while it is running, spray around the intake gaskets, vacuum lines, etc. If you have a vacuum leak, the rpms will increase when you spray carb cleaner on it.
If you have no luck with the above steps, then go to autozone and check out a fuel pressure gauge (and probably a vacuum gauge to double check since you are already at the store) to make sure your pump and fp regulator are working.
If none of those help anything, you are likely looking at some sensor as you have good ignition, fuel, and vacuum, which are three key things your engine needs. Then see if you can round up a scanner.