Reddit reviews Term-LOK TLC310 3 Wire Compressor Terminal Repair Kits 10 Gauge by Packard

If the little "flags" still exist and are still welded onto the pins that exit the compressor, then get new heavy duty fast-on connectors for the wire and push the fast-on onto the flag.

If the flags are gone, get rescue terminals like this:

https://www.supplyhouse.com/Qwik-Products-QT2810-3-Terminal-Repair-Lugs-Bag-10-AWG-2-ft-Leads-w-Nut?gclid=Cj0KCQjwpavpBRDQARIsAPfTwixfDxNIXocFiCotNK0ZcfvFb-J5uviFr9kmSy7qe7TNVXjNGe6BRK8aAnBKEALw_wcB

or this:

https://www.amazon.com/Term-LOK-TLC310-Compressor-Terminal-Packard/dp/B004UW0GGC

Also, check Ebay for (possibly) better prices.

If you want to get going sooner, you can use tie wire to temporarily secure the electrical wire to the compressor terminal.

https://www.harborfreight.com/25-ft-mechanics-wire-97773.html

You need new wires. Something like this https://www.amazon.com/Term-LOK-TLC310-Compressor-Terminal-Packard/dp/B004UW0GGC

As far as contactor not energizing it might be another issue but the compreasor should run if you push contactor in manually. It won't start with those burned wires though. If anything you can bypass the board u till you get a replacement.