Can you provide the model number? It's crucial to what lock you have. The advice below is applicable to the majority of frigidaire washers but not all.

Does it not spin or not drain? It seems like a small difference but it is the difference between a pump and a door lock issue. Your door lock is composed of 2 separate locks, the click you hear when you start it and a 2nd lock driven by a wax motor. If the waxmotor isn't operating it will not do final spin.

Here's how to check:
1) Start the machine in Drain and Spin cycle, empty or otherwise it doesn't matter at this point.
2) The door lock light should be on at this point but the secondary lock will not have engaged until 1-3 minutes have elapsed. You should be hearing drain pump on and off while it tumbles.
3) After 4 minutes if the machine has not begun to spin cancel the cycle.
4) Does the door open immediately?

If the door requires a 1-3 minute wait before opening then your door lock is working normally. If not that's your problem. Very common issue.

Ah so it is a laundry center. Thats why we need a model #. Forget everything I said. Whole different set up. Model # on those is on dryer door edge. If still present.

Was door switch bypassed in the past and the machine working normally? If it's older it has an arm in the door lock that actually closes the lock circuit. That arm must be pushed toward center of machine to close the internal switch or no action. Is that what you bypassed?

We need to determine if machine is trying to power pump? Can you check for 120v at pump when you select any spin cycle?

Also a bunch of these tended to cut wiring up at the top of the washer cavity where it crossed the lip of the side panel. Look for crushed or cut wiring on both sides up where the tub ring could hit.

If no cut wires and no 120v at pump you'll need to drop control panel and see if timer is asking for drain. If I can track down a wiring diagram when you get model # I'll see where to check.

OK, that's progress.
one side of the power to the pump motor goes through the lid lock. So a few questions...
1)What did you do to bypass it, and why?
2)Was it already not draining when you bypassed it?

If it was NOT draining before and after lid was bypassed and the machine does spin, then I'd look for cut, crushed, or damaged wires up where the lid switch wire harness goes along the side of the machine.

After that we need to start working of this diagram to see where the fault is.

Rereading your original post, so it does drain and spin after the wash portion of the cycle? It's just after the rinse cycle?

I'm still curious about that lid lock however, because power to the pump goes through the lock part of it. It has a lid switch for open/closed lid and a lock switch for locked or not. If you called me out I'd change that first.

Some problems are obvious enough to solve by symptoms, this doesn't seem like that is going to be the case.