The blower to my furnace will turn on and blow cold air for like 30 seconds and then shut off and the furnace isn't running. When the furnace kicks on it runs fine.

Is this an old furnace with a standing pilot ? If so the fan switch may need adjusting, this control is in the area above the burners and will have a round dial with arrows, move the on pointing to around 130 up about 5 degrees and see if that cures your problem , this is the temperature that it turns the fan on, Good luck, Mike