Whats my next step?
Time to take a step backwards.

Remove the evaporator cover.
Check the coils .
If they are heavily frosted/iced over you have a defrost problem.
If they only have frost on part of the coils you probably have a low freon problem. It is usually around where the freon enters the evap coils from the compressor.
Since the compressor is running if you have no frost/cooling on the evaporator coils, my guess is that the compressor is toast.
If the frost is fairly even but it is not cooling efficiently check/clean the condenser coils and check that the compressor fan is running.

For low freon and blown compressor, it probably makes more sense to buy a new unit rather than put dollars into this one as both these problems are fairly expensive to repair.

Was it laid down during transport.
If it was It should have been left standing for 24 hours before plugging it back in.

Could well be that it was damaged during transport

It can contaminate the lines running up to the evaporator etc.

Often just unplugging it and letting it sit for the 24 hours will correct the problem. But this is just an often as turning the unit on can contaminate the lines further up.

Is there any way to flush the lines, or is that at the point where you should just get a new fridge?

Probably time for a new unit.
Emptying, flushing and then refilling the freon lines is not going to be cheap.

I would try letting it sit for the 24 hours.