Is there anything else we should check or try before we give up and buy a new freezer?
<Mater> Freezers is
DUMB! </>
Get your voltmeter out, go to town. You'll want to clean the freezer out before you dismantle it.
(A) Is there voltage at the wall plug? 120VAC, line to neutral. No? Troubleshoot that.
(B) There should be a thermostatic control device on the freezer. Mine failed on our deep freezer and I replaced it, see
https://www.sevarg.net/2018/09/30/freezer-repair-and-thermostat-teardown/ See if you have voltage, line to neutral, at the input to that. Set it as cold as possible, see if you have voltage at the output side. If not, replace the thermostat, it's failed somehow. Do yourself a favor and get the solid state type, they're a lot less failure prone than the mechanical ones.
(C) With the thermostat turned down, there should be voltage at the compressor terminals. If there is, and the compressor isn't turning... it's probably time to replace the freezer. You could replace the compressor, but you'd have to pull a vacuum on the lines and be able to solder/braze the connections, and that starts to push even the bounds of what I'm comfortable with doing vs just replacing the thing.