Here's what you need to do:
First hop on the bike, leave the tilt lock on, but take off the parking brake. Then let it roll and try each brake individually to see if it is actually stopping. If it isn't, then your problem is in your brake install. I'm about 100% sure this isn't the case as whether your brakes stop the bike or not have nothing to do with starting.
Next, get a small string/bungee and strap each brake, one at a time, so you can walk to the back and see if the rear brakes are illuminated. I'm betting they're not.
The microswitch is not put in, screwed in, or hitting the brake correctly. They break VERY VERY easily, and are just plastic. Luckily, they're very easy to replace and install, takes less than 10 minutes for both.
Here is more to explain what they look like, etc:
Brake Light Switch