It sounds like it is either not actually firing, or if it is, it isn't detecting the flame. You need to take a panel off and get the exact model number, then you'll have a chance of figuring out what it really needs. But, from what you've said, it seems that it is not lighting or detecting the flame, and goes into a recycle, then tries again.
Depending on the unit, they sometimes have vacuum pressure switches that detect proper air movement. If there's snow or some other obstruction preventing needed airflow, the safety interlock(s) will prevent it from firing. Inside of the cover there's almost always a wiring diagram. Now, understanding it isn't a given...some are a pain with proprietary symbols, and are like trying to read a foreign language. But, that may be your best hope until you can get a user's manual with more detailed help.