2011 Fiesta SES, A/C System, Professional / Mechanic Question / Troubleshooting

2011 Fiesta SES, Air Conditioning issue.

My Daughters car, does not seem to run hot, The cooling fan seems to be operating properly. the issue is the compressor does not kick on as is should. i read somewhere that the cooling fan could be the issue, after inspecting the fan i thought i would wash out the condenser to make sure it was not clogged up with dust, debris. while washing the condenser, noticed the compressor kicked on!! Happy day!! but only for a short while. it ran solid for 30 mins and inside the car was ice cold. but when everything returned to normal "dry condenser" the compressor would not kick on. So i shot the condenser again with water from the hose and again, the compressor kicked on for a short while. the bottom half of the condenser is a bit chewed up from many large insect strikes, gravel but the top half is perfectly fine. i guess it could be the condenser not getting enough air flow? but my question is, is there any other component of this system i'm overlooking. i don't know if there is a temperature sensor that could be possibly faulty and if its something that is replaceable, or if some other component would cause this malfunction. I'm handy and would like to repair it myself. i was afraid the compressor was bad, but now not so sure. any input, insight would be greatly appreciated.
Thank you in advance.