Freezer had frost build-up now worse with no cooling

Freezer was failing to auto-defrost, coils were freezing up in back of freezer. Discovered coils under fridge were very built up with dust and pet hair. We used a small shop vac to remove some build up, then lightly blew the air out to remove the rest.  We then used a blow dryer on low to begin defrosting the coils for a total of fifteen minutes. Unit remained unplugged for two more hours.  Previously plugging it in, the fan and condenser would turn on immediately. This time, nothing can on except the lights inside the unit. We live several hours from town, so repairman or delivery service is pretty expensive. I\'d like to get a better idea of the what\'s going on before I commit to either of those options! I am able to do basic repair myself.