The Most Likely Causes
You've already checked for a few common causes: compressor, fan and airflow. If those are ok, it's time to check for frost buildup. On an automatic-defrost unit, you can't see if the evaporator coils are frosted over, but if you see frost buildup along the walls of the freezer compartment, chances are the coils are choked with frost, restricting the airflow that makes the freezer cold. On a manual-defrost unit, you might see so much frost that you'll realize why your freezer space has been steadily dwindling. Defrosting a manual unit will probably solve your problems. With an auto-defrost unit, defrosting manually can help you diagnose the cause and may get things working again, but you'll likely need a new part or two for a permanent fix.
Other Things to Check
Before you commit yourself to an old-school defrost, check out the following possible causes:
Door seals—you shouldn't feel any cool air when running your hand along the edges of the closed door.
Dirty coils—if you haven't cleaned behind the freezer in years, roll it out and vacuum the backside with a soft brush attachment, to remove dust and debris that restricts airflow.
Ambient temperature—extremely hot weather can make a freezer warmer, especially if you're opening it a lot or frequently adding new items. In very cold weather, a freezer in the garage may heat up, since there isn't enough warm air for the system to work efficiently.