My first guess would be the 'contactor' (relay) used to turn on the fan. I had a bug crawl into mine once and give its life to keep my AC from working. It's a pretty simple fix.

Don't let the compressor run without the fan. This is very stressful for the compressor.

When it first starts up are you getting some cool air coming out of your registers?? You may just have a seized fan motor if the unit is buzzing but the fan isn't turning. BE CAREFUL... but try push starting the fan with a stick when the unit is on... you may have to remove the hail guard to get at it. Sometimes a single push start can unseize the fan for good, other times you may just find out that the fan motor is bad and needs to be replaced.

To weedmeister's point when you remove the cover look for a spring loaded button that should be held down when the cover's on that allows the fan to turn on, make sure it's depressing properly.