Managemylife.com is a great place to find the answers to just about anything, especially on appliances. I would suggest that you provide a little more information such as the make and the model # of your product so your expert will be able to provide you the best possible answer. Just click on reply below and the provide the required data. You can also set service with a Sears technician so you can get this Dryer working perfect again. I have attached the link below. Have a great day!
I may need a few more details to determine the cause of this problem. You seem convinced the vent is not restricted.
I'm not sure what you mean when you say if you put the "hose on does not stay lit."
The flame of a gas dryer burns inside a burner tube. The flame should be concise enough not to touch or trip the hi-limit thermostat on top of the burner tube. If the vent is restricted then the flame spreads out and causes the hi-limit thermostat to trip and shut the flame off.
The flame cycles on and off so quick it never gets hot enough to dry the clothes.
If the dryer works fine with the vent off but doesn't with the vent on then the vent likely has a restriction.
A model number might help me give you additional information concerning this problem. Please reply with a model number for further assistance.