Whirlpool Top Freezer Fridge Not Running Long or Cold

My 12 year old Whirlpool top freezer refrigerator started running warm 3 weeks ago. I cleaned the coils under the fridge and checked the temperature settings. It started up when I fiddled with the temperature and I returned it to recommended settings. I noticed that when it came on it was running very briefly, then it seemed to just stop. I turned the manual switch on the Defrost Timer and everything seemed almost normal for several days (just soft ice cream) and then the fridge and freezer warmed up again. It was starting up and running for three minutes at a time with a long time off. I replaced the Timer and it all ran again, just a bit warm, for a few more days. Now it’s running just long enough to maintain 40 degrees in the freezer. The start relay is good. No frost on the coils behind the freezer compartment. When it runs the compressor is running (vibrating) and so are the fans. Cold air is coming into the freezer but it all runs just briefly. The compressor feels hot when I touch it but not so hot I can’t leave my hand on it. I followed the flow chart. Is it time to get a new fridge?

So…It’s 4 days later and I’ve received no replies to my post (above). After I posted the refrigerator stopped running completely for two to three days and the freezer came up to room temperature. This morning it started running again while I was making coffee and 11 hours later it is still running and quite cool in the freezer. I have ordered a new refrigerator, but the mystery is driving me crazy. What is making the old Whirlpool work so inconsistently? Can I fix it? Does anyone have any ideas?

Again… A few days later and the drinks and things I’d put in the freezer to keep them "cool" when it started running again are frozen solid this morning. I don’t know what to think. Is it likely to keep working for a while? It doesn’t make sense – does it?