[Reyrd]

My Admiral Capacity plus dryer just keeps drying. It never times out. Also, it may be over 10 years old. I've lost track of it's age. What part do I need to repair this?

[denman]

Here are your parts.
Replacement parts for LNC7766A71 models | AppliancePartsPros.com

What part do I need to repair this?
Cannot say you will have to do more troubleshooting.

Does it not time out in both auto and timed dry modes?
Does the timer advance at all?

Most units use different circuit paths to power the timer motor in auto and timed dry modes. So if it does not advance in either mode then odds are the timer is shot. This can be confirmed by measuring the voltage across the timer motor. If it is getting 120 volts (some units use 240 volts) and not advancing the timer need replacing. Be very careful when doing this as there is 240 volts at the timer which is lethal.

If it advances in timed dry but not auto then your problem is probably elsewhere. On most units the timer gets power when the heating coil shuts off in an auto mode. A common cause of no advance is a grounded element re: it never shuts off.
Check the heating coil.
Unplug the unit and both wires to the coil.
Check it with a meter, should be around 12 ohms.
Then check from each side of the coil to the case/frame, both should be infinite ohms (open). If not the coil may have sagged or broken and is touching the case. This can cause it to run and the thermostats cannot regulate it.

If it does advance to off but never shuts off then I would say that the timer is the problem re: the on/off contacts in the timer are welded together.