If you can, take some pictures of the wiring under the driver's dash area and post them.

 

Will do.

 

Ok, there are several things "in play" here.....an aftermarket alarm, ect.

Sounds like you have a volt meter as you gave the battey volts as "12.2v". So pull the small wire off the starter solenoid and try to start the car and measure the voltage on the small wire - what is it?

A battery can have "good" voltage but not have the amps needed. It wouldn't hurt to pull the battery and take it to a parts store and have it tested under load for volts and amps. This would also be a good time to clean the cables since the battery is out.