2004 mercury sable no tension in gas pedal

SOURCE: 98 mercury sable transmission

Check your transmission fluid. You could be alittle low. Check it hot in Park while running.

SOURCE: AWD acting like all wheels are locked up

  The clutch in the transfer case is burnt up and fused together therefor binding the powertrain. If you continue to operate it like this it will destroy the front differential and possibly the rear differential. It was most likely cause by the tires not having equal circumference either due to a mismatch of tires (different brands although the same size is indicated on the side wall will have different measurements,I have seen BF Goodrich tires have a different size because speed rating was different although the model was the same) or lack of tire rotation during the life of the tires.. If the measurements are not with in 1/4 inch around the center of the tread this will cause your concern. Tires should always be replaced at all 4 corners on all wheel drive vehicles.

SOURCE: Check charging system icon keeps coming on

I had the same problem with a 99 sable and it was the drive belt

SOURCE: 2002 Mercury Sable-shakes with acceleration

You describe this as an acceleration problem however, if the car does throw a check engine light it should be recorded in system memory so it can be pulled by scanning with and OBDII scanner. It sounds as if the car is being starved for fuel on acceleration. Check the fuel lines for kinks as well as check the fuel pressure. The problem could be a faulty fuel pump that has yet to completely die.

SOURCE: 2000 mercury cougar hesitating/jerking

First, disconnect neg battery cable 10 minutes and reattach to clear codes.
Lean condition means it is not getting same fuel as other side of engine.
Since you had it scanned before, try Autozone to see if new results.
You might try a TPS switch which regulates spark and fuel feed. At lower speeds EGR starts to open-you should have code for a problem there.