Help! Fridge not working properly

Play by play of where I am now:

• Go to make a sandwich and I grab a beer
• Feels oddly not-cold
• Take my cooking thermometer and stick it in the fridge for a min.  64 degrees
• Pull fridge away from wall 7 unplug.
• Take off rear panel and front intake panel.  This is a fridge with a bottom freezer and the coils are below the freezer. 
• Coils are absolutely caked with dust.  Obviously this is a problem.  
• Got a vacuum, paintbrush, and dragged my compressor & air nozzle upstairs to clean it out the best I can (its damn near impossible to reach the center of the coils).  Its not 100%, but probably 98% clean now.
• Plug it back in.  I can hear a fan running inside the freezer, but nothing related to the compressor is running.
• Unplug again.  
• Remove overload relay.  Shake it (internet recommended this) but it doesn't sound like anything inside it has failed.  Its not 100% solid, but it sounds like a loose-fitting metal contact does on other stuff - like european/us A/C adapters.
• Put it back together and plug it in.
• Still just have the freezer fan running, but no compressor kicking on.
• The compressor feels warm to the touch but not hot.  

What's my next step?

Drink warm beer.

we're dealing with a fridge problem too. freezer is cold but not freezing cold, fridge side is cool but not cold enough. it's over 10 years old so it's out of warranty. i dunno anything about fixing it so we either hope a repairman will call us back or we check for used ones on craigslist.

it sucks.

Does it have a timer for the defrost?  If it does find it and you should be able to turn it manually to see if it is stuck in the defrost period. 

I can't find any settings for defrost, but that cycle should only last a like 30 mins though.  It's been plugged in again for an hour or so.

Yes, but the timers stop working and get stuck in defrost or chill. 

Evaporator was frozen solid.  Appliance guy cleared most of it out with a heat gun, but there is a nice solid block around the heater inlet for the defrost and I have to let it thaw another 24 hours or so before I can plug it in.

I have saved some meat and cheese, but pretty much everything else is going in the trash :/  On the plus side, its a good time give the inside a deep clean.

The main issue is likely the intake of warm air from a door not sealing properly.  The RH door has material bubbled up on the top where it should be flat (manufacturing defect or something) but I didn't catch it under warranty.  If the door is left to close under its own weight it will often get stuck.  I might have to see if I can tweak this area with a heat gun or something.  A new door is $7XX 

Is your refrigerator running? Better catch it before it gets away!