What could be wrong with furnace? Furnace works fine with utility power, when you hook up a generator the?

If I am you, I would install the transfer switch (that allows you to safely connect a generator to your household wiring.) for you and your home’s safety. If your setup allows your main breaker to still be turned “ON” while the generator is back-feeding into the panel then your installation is illegal and extremely!! dangerous.

Check the rating(size) of ALL the wiring accordingly, based on your equipments and follow your local codes. According to your info, you ran size of #14AWG (American Wire Gage), it is only good for 15 ampere which is only good for total load (continues load, if it runs over 3 hours) of 1,440 Watts (15amp x 120volts x 0.8derating factor).

Good luck!!

excuses my grammar/ spelling

are you checking at the furnace during it's attempt to power up? How long is the wire from the generator to the furnace and what is the gauge of the wire? You'll see voltage drop over a distance, especially if the gauge is 14 as are many extension cords.

well this might sound like a stupid suggestion but

for shitz and giggles can you run a known to be true ground wire

to the furnace.

you have 120v going to the furnace but what is the furnace rated for 120v or 240v

Black = power

White = neutral.

Reversed polarity??