My Indesit WIDL126 washer/dryer doesn't dry clothes

Dryer temperature sensing fault (washer dryers only)
Issue: Washer dryer is not drying clothes.
Advice: We recommend you call our customer service centre to book an engineer on: 0344 822 4224

Simple ! As you say button stuck and you can't get it to operated, so get a new button fitted

the heating element of you dryer broken already

Had the same problem, very hot but wet clothes. This is a condensor drier. The fack that the clothes are hot rules out the heater or its control. If yoy hear the fan running and there is no blockage the fault is caused by the 3 stage water valve. During drying a small amount of water is passed through a condensor chamber, the cold water causes steam the condense backi into water then is pumped out through the drain. If the water valve fails no condensing takes place and the clothes remain wet. The valve is easy to change and costs about 15 pounds.

most likely a clogged up vent

I am having the same problem on a WD9900A. The wash cycle works great. Spins fast and clothes are completely rung out. Dryer cycle heats up well. Fluffs and heats cloths. At some point during dry cycle water is injected on clothes and they end up sopping wet; much wetter than after wash. Filter is clear. Outlet pipe clear and functions well. Possible problem with dryer timer? Or washer timing kicking back on?

This problem is normally caused by either the thermostats not working properly or the heating element is the problem.
Both are normally located in the air tube of the dryer down stream of the blower.

http://www.instructionsmanuals.com/u2/pdf/lavadora/Indesit-WIDL126-en.pdf

my washer works fine but the dryer wont heat up or dry the clothes it goes onto dry but all the clothes are still coming out wet and the drum is cold

look for debris in the filter,
remove the bottom front panel ( 3 screws on bottom)
Unplug washer ,
open the large access filter screw on in center , be ready for excess water to spill on floor, clean filter and be sure the pump impellers spin freely.