
Stabbing in the dark here. IF the mechanic jumped the starter by applying 12V directly to the starter and it worked, then there are 2 things possible.
1. You might have a bad starter relay, not to be confused with the starter solenoid. Trace the heavy 12V cable from the starter back through the chassis. At some point you will come upon the relay. It has a heavy cable going into both sides, with generally 2 smaller wires going to your ignition switch. These go bad very frequently and are cheap to replace, but somewhat hard to find.
2. Check for a possible blown fuse (unlikely) somewhere upstream of your starter. Again follow the heavy 12V cable from your starter back to your chassis and try and find where it terminates (probably a fuse block somewhere around your firewall or under the dash.
If I read your post correctly, if the mechanic "jumped" your starter by applying 12V directly to the starter motor and it started, the your solenoid is fine.