Hello,
Welcome to FixYa.
Based on what you've described, and provided the unit is draining ( and I mean the drum is clear of water aside from the items being soaking wet )...you likely need a door lock/switch assembly.
**The door latch is likely the single most common fault (which prevent's any spin, and consequently drenching wet clothing at the end of the cycle) with the frigidaire/electrolux built washer's, ASIDE FROM PUMPS BEING OBSTRUCTED.**
I think it fool's many people because the lock indicates it is energized on the panel, however the built in "monitor" switch inside the assembly fail's. I do see a lot of these particular machine's...unfortunately.
You should be able to purchase one at most local brick & mortar stores or on-line part's depot's such as "searspartsdirect.com" "repairclininc.com" to name a couple. They usually sell for about $50 or so, part # 1531974 ( # at repairclinic.com ) and are relatively easy to replace. It should resemble the image here... 
As for replacing said switch, There are a couple ways to access it, through the top and squeezing your arm down the front or the way I prefer, remove the front bellows spring/retainer.
1) **UNPLUG THE WASHER FROM THE WALL OR TURN OFF THE BREAKER...SAFETY FIRST.**
2) Remove the spring, get it started where the spring is located with a small screwdriver. Once you`ve got the spring/retainer off ( it comes off and on pretty easy by hand ) pull the gasket/bellows back away from the cabinet. 
Will not spin during spin - 309723c.jpg>
3) Undo the two screws holding the switch to the cabinet, pull the switch out ( there is just enough slack in the wires so don`t pull too hard ) and swap the wires from the old assembly to the new oneWill not spin during spin - 46e20c7.jpg in business.
4) To put it back together, just reverse the removal procedure. The trickiest part is the retainer. Rap the retainer around the boot leaving the spring for the last...and make sure the spring is located at the 6 o`clock position...usually. Just wherever it was initially.
Let me know if you need further assistance going forward or if my instructions are not clear.
P.S.
There is a slim chance of a faulty motor or motor control board, but that would not be where I would direct you to start...those are exceptions rather than the rule.
Thank you for visiting FixYa today. Good luck.
Regards,
Macmarkus :)
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