Dryer only runs if I hold down the start button. It had been making a high pitched squeel leading up to this.

Here are your parts.
Parts for Whirlpool GEW9878LW0 Dryer - AppliancePartsPros.com

See the attachment for the tech sheet.

It is probably either a motor relay problem or a control board problem.

The easiest way to check the relay is to swap it with the heater relay.
I think they are the same but you should double check this.

Also would not hurt to check the relay coils to see if they are the same. I do not know what the resistance should be but they should be close to each other. The reason for this is that if the relay coil is shorted it would blow the board.

If no joy check that the Start Sense from the thermal fuse to the board is OK (0 ohms).

If the above does nothing then I would replace the board.

You should also track down where that squeal is coming from and repair it.
Possible causes are the idler wheel, the front drum support or one or the rear support rollers.
Also check the blower to be sure nothing has dropped in there and is rubbing on the blower wheel.
Worst case scenario would be bad motor bearings.