What is the part number for the griddle gas valve on my Dynasty DGRS-36-4G ser 280898 0

I'm not familiar with your particular appliance but all gas fired appliances have a thermocouple and igniter.

the thermocouple is designed to allow/prevent the gas valve from opening.
They commonly go bad on stoves and hot water heaters.

should you wish to attempt a repair yourself l
look on the Internet for a picture of the thermocouple for your unit , turn the gas valve off, then attempt to clean the thermocouple first with some medium grit sandpaper. Just some gentle rubbing a few times can take carbon buildup off.

Then try the start proceedure again. If the pilot light or burners do not light the the thermocouple is the least expensive component I can think of to repla e. usually less than $20 and very intuitive to do.

if that does not work depending on your ability you may either need to replace the igniter or gas valve. Or. Call a pro.

Be safe and keep the gas valve on the unit off until you are ready to restart each time
Hope this helps

Check for plugged orfices, usually grease build up cause these problems

Replace the ignitor; it is worn out. It is not like a light bulb where it goes out totally.

Here is the factory (Dynasty / Jade) ph # 800-884-5233

I think you are talking about the oven safety valve or thermal valve. before you change you oven safety valve, I would check the Amperage on the oven ignitor first, install AMP meter on one of the ignitor wire, it should draw above 3AMPs, if not then you have problem with the oven ignitor and not the safety valve. we hardly change the safety valve, I'll try to change the ignitor first. Have fun.

Bad oven ignitor, to check it, turn on the oven, check Voltage on 2 ignitor wires, it should have approx. 110v, if yes, change the oven ignitor, if not then check oven safety valve of oven thermostat, but 90% is the oven thermostat. also make sure the oven tube is not corroded at the ignitor area, if so, change the oven at the same time. Have fun.

part number for the griddle is WB31K10140
partstore.com has it for $87.95 hope it helps

I have a Thermador Gas Range PG364GDBS - Oven, 4 burners, and center griddle. All are gas. The four burners and gas oven work fine. The griddle just stopped working, no spark. Turning on the griddle control, the gas valve opens(hear it), gas flows (smell it), but the ignitor will not spark (no loud or faint spark that I can hear). I got a replacement ignition device (mount at the burner) thinking it might be the problem, but still no spark. I checked the AC voltage at the terminal and measured 39 VAC between the terminal and ground. Not sure if that is the correct voltage. Any insights or advice would be great.

it's very possible that the mice may have gotten in but i would say it's the ingnition electrode.

i would have a technician come and take a look. check you local authorized repair shops. shouldn't cost you more than $150.00 to repair it.

This addresses the cleaning question only. I was a chef for 27 yrs.  Once the griddle surface has begun to rust, and this can and even will be the case on a new stove, you have to get agressive with it. You're going to use sanding tools and oil. 
If the griddle top is heavily rusted, I use my electric palm sander fitted with fine emory paper (the black stuff that can get wet). Wet down the surface with a small amount of oil and work the sander evenly over the entire surface in rhythmic strokes from front to back or side to side. I don't have a scientific reason for this but my gut tells me not to work in circles or random strokes. Try to work the entire surface evenly to avoid creating high or low spots. Use a straight edged spatula or I use a dough cutter (flat edge of about 4" and available from culinary store for under $10) to cleanly scrape  the dirty oil off the surface. Sand in shorter durations & clean often to avoid grinding dirty flavor into the surface. 
Once you have it clean its time to season it. With a better oil focusing on flavor, spread a thin layer over the surface and cook at about 250 degrees for 15 - 20 minutes. Repeat this after every use until you build up a layer of cooked oil almost like enamel to resist rust between uses. This makes a teflon like finish to your griddle.
For regular use and cleaning scrape down immediately after cooking and while the griddle is still hot. When its cool use a hand sanding block you can get from the hardware store. The one I prefer is a firm sponge with emory paper wrapped around it. I store this in a bowl on the shelf above the stove because it is oily and dirty. Alternately you can also use rock salt and a kitchen rag to loosen food particles stuck to the griddle but this makes for messy laundry or throw away rags. We also use viengar or lemon juice and water to loosen food while the griddle is still hot or warm. NEVER USE SOAP!!!!!! You want your food to taste good don't you?
The oil used for cleaning can be anything with minimal flavor like canola oil but the oil used for seasoning the griddle should be a high heat type like sunflower.
Personally I only cook in black cast iron pans and the above method is how I treat them as well. Rock salt and water is all I ever need to clean them between uses.
Rick Casey