Is the problem that it will light the pilot, light the burner, then cut off the burner when the main blower motor kicks on, or if it stays lit after that, cut off at random?
If so (and if it was just the serviceman who told you the fuse was blown), it probably WASN'T the board at all, but rather the flame sensor. It only has a 1-wire connection, and grounds through the plate to which it is mounted. Corrosion develops between the sensor and plate, causing a failed ground, thus breaking the circuit and appearing to the logic board as if no flame is detected. This cycle will repeat 3 times then the furnace will go into a lockout for 1 hour, at which point the LED on the control board indicates 1 blink. The fix is to remove the flame sensor (not easy to get to, but I've managed it), clean off the corrosion from both the sensor and the plate, then reinstall the sensor (lacking proper tools, I cleaned mine by scraping with a flathead screwdriver). I've needed to do this about twice a year, I've seen some people on here say it's a monthly occurence for them.
According to a friend of mine who owns several rental properties, he has encountered this problem frequently, but I'm not sure what brands he has installed.