The pilot light is called an ignitor and I assume you're looking at it through the small square opening on the front panel.
If the ignitor glows and then goes off with no flame then the problem can be with the gas coils or the gas valve itself.
The ignitor should cycle on and off and if it glows then the thermal fuse, thermostats and timer are all okay.
Keep in mind that new dryers will start in the $300 dollar range.
If you are comfortable with do-it-yourself I may be able to offer you an alternative to an $200-$300 dollar repair or a $350 replacement.
The problem will be the valve ($101) or coils ($80) and if will be difficult to determine which one it is unless you can check resistance with a meter.
The option I would offer is if you have no meter and you don't want to spend $129 dollars for a technician to come out is to replace the coils as a do-it-yourself.
The coils individually about $35 dollars each but for some reason I've never understood myself the coil kit 279834 with both coils cost about $21 dollars.
You can get the 279834 kit at the following link:
The image below will show you how to access the gas valve.
Remember to unplug the dryer first.
Read through the instructions and see if this is something you feel comfortable doing.
If you do not feel confident repairing this problem yourself, then you can have it repaired at your home by a Sears technician. Here is a link for the website:
Sears Home Services
I hope this information is helpful to you but if you have other questions then we can offer you further assistance.