My furnace is working and the pilot is lit. the fan will run when I turn it on. The heat is not coming on but if I switch to air conditioning and lower the temperature on the thermostat, the air will work. Is this a furnace problem or with the thermostat on the wall, I only have the one. The fuse box is fine also nothing tripped?

It could be either. Remove the thermostat. Jump from the Red terminal (R) to the White terminal (W) and see if the heat comes on. If so, you have a bad t-stat. If not, then I'm guessing the gas valve is bad. But to verify, take a voltage reading across the terminals on the valve when the thermostat is set for heat. Should get 24 volts. If you have 24 volts and no flame, then the valve is bad...

Is your furnace new enough to have forced draft? If so, go to the great sticky, https://www.askmehelpdesk.com/heating-air-conditioning/heating-cooling-maintenance-repair-troubleshooting-frequently-asked-questions-58313.html and start with sequence of operations. The gas isn't going to come on until the controls receive a signal the inducer blower is working. There are instruction on checking it.

Pilot is lit...

Is your furnace new enough to have forced draft? If so, go to the great sticky, https://www.askmehelpdesk.com/heating-air-conditioning/heating-cooling-maintenance-repair-troubleshooting-frequently-asked-questions-58313.html and start with sequence of operations. The gas isn't going to come on until the controls receive a signal the inducer blower is working. There are instruction on checking it.
I'm pretty sure the furnace is the original from1987. The fan works and the AC works, the pilot is lit .

Pilot is lit....
Yeah and the AC will run if I switch it on just no heat

i'm pretty sure the furnace is the original from1987. the fan works and the AC works, the pilot is lit .

I can't say for sure if it would be a newer one. Look at the vent pipe where is comes out of the furnace. If it is 6'' or less, chances are it has a draft inducer. Have you changed the filters? If it has a circuit board with lots of wires inside near the filters, chances are it is a newer one.

If so, the first thing when the thermostat calls for heat is for the small draft inducer blower to come on. Not only must it run, but the pressure switch must tell the controls it is running. As I said, go to the sticky. Northern Heat has already done a bettter job explaining what you need to do than I can. If you have trouble understanding it, post back with specific questions.

The fan will only work for a/c or fan only.
2 possible problems.
Spill switch witch is a heat sensor between your chimney and furnace.
Roll out switch
Inside the furnace neer the burner tubes.