Here are your parts
Replacement parts for WHIRLPOOL SEDS800HQ0 | AppliancePartsPros.com

Here is the wiring diagram
http://www.servicematters.com/docs/wiring/Wiring%20Sheet%20-%203406687.pdf

It could be a number of things, just replacing parts without checking them will just cost you a lot of extra money so it is best to do more troubleshooting.

If by stopped drying you mean that the unit will not run at all then:

1. Try flipping the breaker off/on slowly a couple times, sometimes you can loose half the line without actually tripping the breaker.
If this does nothing, check the voltage at the plug
L1 to L2 should be 240 volts
L1 to Neutral and L2 to Neutral, both should be 120 volts.
If OK
Unplug the unit and check the wires at the terminal strip in the machine to make sure none are loose or burned out
If OK
Check the power at the terminal strip.
[COLOR="Red"]Be careful as 240 volts is lethal !!! [/COLOR]

2. Check the motor's thermal fuse (Item 7 in Section 3). It should be 0 ohms.
A jiggery pokery method is to unplug the unit, remove the wires from the fuse and short them together, tape them together so they cannot short to anything else. Plug it in and give it a try. If it now runs replace the fuse ASAP as this is a critical safety device to prevent lint/house fires.

3. Check the door switch and the push to start relay contacts.

If by not drying you mean it runs but has no heat:

1. Do step 1 from above.

2. Check the heating coil, should be approximately 10 ohms.

3. Check the heater's thermal fuse (Item 9 in Section 3).
If it is blown you have to find out what caused it to go.
Note: that sometimes they do just blow on their own but changing it without checking other things is a gamble. I beleive richappy (another regular poster on this forum) has done a study on thermostats and found a wide variation of actual trip point and what is specified.

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 on high and the thermostats cannot regulate it.

If the above is OK then you will also have to replace the hi-limit as it should have regulated the temperature so the fuse did not blow.

You still have to find out why it blew.
Check that the belt is OK.
Check the seals (drum etc) in the unit. The air is pulled over the heating coils, through the drum and pushed out the exhaust. So any large seal leak will pull in room air and the cycling thermostat on the blower will run the unit hot.
Check that the lint filter is not coated with fabric softener residue which greatly reduces air flow.
Check/clean your vent system.
Check/clean the blower wheel.

If all OK you may want to replace the cycling thermostat as it's contacts may not be opening (welded shut).

4. If the fuse and heater are OK check the other thermostats in the heater circuit.

Since your problem started with long dry times you should also clean/check your vent system.
Also a good idea to give the interior a good cleaning, including the blower wheel.

If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.

There is a good STICKY at the start of this forum about it's use.