Horn doesn't work after sitting for a year. Checked fuses, and wires to horn

Started about 3 months ago. As engine gets hotter, starts get slower. Turn key to start, it makes noise (kind of a groan) about once per second, then it will eventually crank and start. When it doesn't, a jump start will start it. Just replaced battery. Alternator and ignition module is fine per AutoZone. I have read fuel pump or regulator might be problem. I will listen for this now. Check Engine light often comes on. Seems to be missing a little at highway speed.

For a long while the engine would just stop (while driving down the road or at park/idle). I could (when driving) pop it in neutral start it and keep going. It has had the crank sensor replaced. Now, when I turn the key, the pass key light flashes rapidly and is accompanied by a relay chatter coming from the relay/solenoid panel behind the passenger side kick panel. Then one day after the car sat, the horn just started blaring. I thought the battery had lost its charge causing that(don't ask me why). So I brought the battery back to a full charge, tried to start the car again, with the same light and relay chatter results. Then about 2 hours later the horn went off again. This is a very sound car - mechanically, but this electrical problem is driving me nuts. Any suggestions?

In park it idles low and wants to stall and when idling in drive it acts like its out of gas and bogs down and check engine light comes on

runs good @ hard acceleration. stumbles on partial acceleration. engine light code indicates icm. replaced icm, coiles, wires, plugs, fuel filter, tps, cleaned maf, checked fuel pressure, cleaned all electrical connections I could find. no positive results. what is left?