The short white wire that you describe sounds like the neutral ground wire shown in the first image below. The left picture in this image shows a 3 prong dryer plug installation and the right picture shows a 4 prong dryer plug installation. You should be able to
unplug the dryer
and reconnect this wire properly on the terminal block.
This loose wire should not cause your heating failure. A loose black or red wire on the terminal block would cause a heating problem. Make sure that both of these wires are secured properly. Also, I recommend checking the breakers for the dryer outlet. The dryer will run if only one of the 120 volt legs (normally supplied through the black wire on the terminal block) of 240 volt power is supplied to the dryer. If the second 120 volt leg (red wire) is missing, then the dryer will not heat. If the breakers are okay, then I recommend checking the voltage at the dryer outlet using the diagram in the second image below. NOTE: You should only check this live outlet voltage if you are completely confident in your technical ability to safely measure it using a volt/ohm meter.
If the outlet voltage is okay, then you could have a failed heating element, a bad heater relay on the electronic control board, an open high limit thermostat, a failed motor centrifugal switch or a wiring failure between the components in the heating circuit. A failed thermistor (temperature sensor) could also prevent the dryer from heating. I recommend calling a service technician to diagnose and repair these types of failures.