Driver side seat belt is stuck and will not 'unlock'.

2005 Towncar SRS Code 33 (3 flash + 3 flash, repeat this set for twice. then Beep 5 times pause x 5 = 25 beeps every 30min).

This means you have problem with left (Driver) side pretentioner (Seat belt retract system).
It doesn't mean physical belt or retract mechanism.It is just bomb wiring which is part of airbag system.
When airbag deploy, passenger must stay tight in seat otherwise body lean to front then slam back to seat by airbag.
if belt is loose or delay to lock, passenger's body rocks back and forth.So, system use small bomb (Fire power) to lock and retract seat belt when airbag deploy.There is small bomb and igniter in part of Seat belt retractor.
Code 33 is warning for this part on 2005 Towncar.(older model is different meaning in Ford/Lincoln, it's possibly passenger side airbag system for earlier model)
Before you work for any part of Airbag system and touch any "Yellow connector", * *Disconnect battery (negative side is good enough) and wait at least 5 min to clear all power in system**.(Airbag store back up power for few minutes to be able to deploy even in case if power disconnected)
by the way, you should move your driver seat most forwarded position before you disconnect battery to make it easy to work with seat belt.
locate driver side seat belt retractor (in center pillar between front and rear door, you may have to fight with weather strip)

Locate Yellow connector on bottom of Seat belt retractor (it's called "Pretensioner")it is located on very bottom of rear side of retractor.
only one yellow connector. (make sure your battery is disconnected)
Check its physical connection or looseness.if connection looks fine, you may have to replace whole seat belt ($180-$200 in Lincoln dealer)
You can check if pretensionor is good or bad by regular tester, but unless you know how, I won't tell (because I don't wan't you to blow out pretentionor).

Try sliding a thin long metal shim such as a butterknife in between, you may have to "Pickthe Lock",once it unlocks, you'll need to go see "Yard" for a used retainer that has 1 big bolt thru the floor, under the seat

they have a mechanism called a seat belt cam which is gravity activted with force and usually at 15mph and with sudden braking the cams should lock. If u feel that they have to much play and seem like they dont lock properly id suggest changing both belt assemblies because the cams do wear or get stuck and fail like any other moving part and it is a saftey issue for u so better safe than getn injured with a faulty belt.

possibly there is something stuck in the belt not letting it retract

Unfortunately the seat belt must be replaced the mechanism that control it is stuck and cannot be release.

Check under the seat where the guide rails are and look tovsee if the wire underneath is pulling to release both sides of the seat on the rails or one side. If it's not releasing both sides you have to check to make sure there is nothing stuck in the guide rails (coins perhaps). If all is clear you'll have to adjust the rod or cable that attaches to the lever of the seat to make it release both sides so the seat unlocks and moves easily.

No one can fix it!

Don't you find that odd?

You remove the plastic seat belt retractor covers,
on the floor by the "B" Piller

If you need to replace them, the retractors I mean, there
is a special GM Torx Driver Bit for seat belts

I would play around with them to see what the issues are

IF THEY HAVE AN AIR BAG INVOLVED e.g. SRS
System integrated into the seat belts,disconnect the battery
(before) you even think of going near the covers

1. Make sure you have the anti-theft codes for the radio and the navigation system, then write
down the frequencies for the preset buttons.
2. Tilt the steering wheel all the way up and telescope it all the way in.
3. '04-07 models passenger's seat: Carefully insert the tip of a small screwdriver (A) through
the hole in the back of the front seat belt lower anchor cover (B) and into the hole in the
front seat belt lower anchor (C). Unlock the lower anchor by pushing in on the screwdriver.
Remove the screwdriver, and then detach the front seat belt anchor plate (D) and anchor
cover from the lower anchor.4. Slide the seat all the way forward, then remove the seat track end covers from the back of both seat tracks.5. Slide the seat about half way to the rear so you can access the seat mounting bolts. If equipped with the driver's 8-way power seat, fully raise the seat.
6. If equipped with a side airbag, disconnect the negative cable from the battery, and wait at
least 3 minutes before removing the seat. 7. Remove the bolts securing the front seat. 8. Lift up the front seat, then detach the harness clip and disconnect the connector.
If equipped, the seat heater connector on the 2-way power seat and passenger's
manual seat. '04-07 models, disconnect the seat position sensor subharness connector on the
driver's manual height adjustable seat and the driver's 8-way power seat.
9. With the help of an assistant, carefully remove the front seat through the front door opening. 10. Install the seat in the reverse order of removal, and note these items:
Apply medium strength type liquid thread lock to the front seat mounting bolts
before reinstallation.
Make sure each connector is plugged in properly.
Tighten the seat mounting bolts to the specified torque in the sequence shown.
Slide the seat all the way back and tighten then slide it forward and
tighten Before attaching the lower anchor bolts, make sure there are no twists or kinks in
the seat belts. 04-07 models passenger's seat: The triangle marks on the anchor plate and
the lower anchor must face the same side. Insert the anchor plate into the lower
anchor, and make sure that it is locked securely. If equipped with a side airbag, reconnect the negative cable to the battery. Enter the anti-theft codes for the radio and navigation system, then enter the radio station presets. Reset the clock. Your all done. Drink a cold beverage and enjoy the rest of your weekend! hope this helps. Dave

If it's iced up, try a hairdryer or some rubbing alcohol.

If brute force doesn't unstick it remove the back seat and pull the cover off of the reel. The problem should be apparent. You can turn the reel with a large screwdriver if need be.
If the belt is damaged find another one at your local recycler, the side reel is behind a plastic panel that is easily removed, the assemblies are held in by big bolts.