My whirlpool imperial dryer no longer starts, the dryer was working fine, today when I press the start button I get nothing. Are there some basic troubleshooting steps I can take to try and trace the problem? I am happy to get out a multimeter.

Look at these sites and follow these instructions: http://www.electrical-forensics.com/Dryer/ElectricClothesDryers.html
http://fixitnow.com/wp/2010/10/09/whirlpool-dryer-model-le5800xsw3-wiring-diagram/

You will have to take it apart and test the thermal fuse near the heating element. You will have to clean the drier out thoroughly or it is all for nothing. Every air duct will have to be removed and scraped and washed out to remove baked on lint deposits which is like a concrete lining. This will burn so the manufacturer has installed the safeties to keep from having a house fire. Driers were the number one cause of fires at one time. Look at: http://www.youtube.com/watch?v=MMP7BW1lLs4 to see how. Also: http://www.youtube.com/watch?v=iBiRw-KElC4 ; http://www.youtube.com/watch?v=yFTZGgVisCI
When you finish cleaning the drier and install a new safety or element it is best to also replace the belt, too, because you do not want to have to disassemble it again and if the belt is over two years old you should replace it. The safeties are oval-shaped with a round center part containing the safety with two plug-on terminals for the wires.
Using an ohm meter you put a lead on each terminal of the safety with wires unplugged and if it's good you will have a reading of about zero; if it's bad it will read infinity.
Note that on most of the videos it does not show them washing out the parts, but this is important because it's the only way to really get the parts clean, just don't get motor wet or the capacitor if it has one. Vacuum out the motor. I would move the drier out to your garage to have plenty of space to work. You also want to check your vent and clean it, also. The job is really easier than it sounds. There is no shortcut that will work; it has to be cleaned well. Before you re-assemble it make sure to use white lithium grease (high-temp grease) and grease all bearings. Just vacuuming out the dryer a little does little good. DrTom4444

So I tested the thermal fuse and it was blown. I was able to pickup a replacement in town, I disassembled everything I could and cleaned it all out, it really didn't seem to have much in the way of buildup. Now that it is back running it seems to just be on heat continuously. I can't figure out if I need to replace the thermostat at heater element or the whole switch/thermostat unit that controls temperature. Thoughts?

The model number is LE7000XKW0 I was able to find a parts diagram here http://www.appliancepartspros.com/partsearch/model.aspx?model_id=252234 I am thinking I need to replace either Part 79 from the console section(688710 thermostat) or 15 in the bulkhead section(341195 thermostat 250 degree)

Use your meter to decide what needs replacing. If you did not find much buildup you were not looking in the right place. Look at all parts that move air and remove the parts and clean them. DrTom4444