Today is Dec 20, 2015. Your question was posted Nov 23, 2015. Within that time period, I presume you have had it repaired? If not, here's what I think based on the information you have given. It could be just dirt, dust, soot, or spider nest on the photoelectric (light sensor) cell. Your instruction manual should tell you where it is. Just open the heater and wipe the lens. The photoelectric cell (some manufacturers call it a CAD cell) looks to see that there is a flame. Your heater will fire up and after a few seconds, the computer checks to see that there is a flame. If no flame, it shuts down the heater. That sounds like your situation. So, if a spider has laid a nest over the little plastic circular window of the photoelectric cell, then the light from the flame cannot be sensed and your computer circuit board will shut down the heater. If cleaning the photocell sensor doesn't help, then it might need replacement. That's pretty cheap. Just get your part number from the instruction manual and plug that number into google to find some online dealers. Or, actually, eBay is a good place. Just plug your part number into the eBay search box. Lots of heater dealers sell through eBay. If it's not the photocell, then it could be the circuit board. The photocell is usually less than $20 so that's a good place to start. The control circuit board runs $40 to $100 depending on heater model and depending on the dealer's discount structure. There is a test device that shops use to determine if the photocell or if the circuit board is defective but the tester costs way more than replacing the circuit board and photocell so for people like you and me, it's cheaper to start replacing those parts. I think it is quite likely that your problem will be solved by cleaning the photocell lens. But, also, before replacing the photocell, be sure to check that the wires are intact from photocell to the circuit board. If a little critter like a mouse or squirrel got into your heater, they might have gnawed the wires in two. In that case, you could just repair the severed wire. Sound funny? Yes. It is but it's the absolute truth. Just like a human that bites its fingernails, some little critters will chew through wires and such just because they are there. (Just ask my sister why her Toyota was running rough...yes...something chewed through two of her spark plug wires!)
I don't know what your technical skills are. YouTube can be your best friend here. There are inexpensive ways of testing the photocell with a very cheap multimeter. Those videos can help you. It is also possible to replace some components on the circuit board if you are handy with a soldering iron.
Count your blessings, though. Your heater will fire up for a short period of time. That means that your motor, transformer, igniter, and other parts are in good working order. And...there's a good chance that just cleaning the photocell will get you back into full working condition.