I have PLPD, but the other driver was at fault, can I sue the driver that has full coverage

Your state has special laws regarding PLPD and you can recover $500 max under your states laws. I recommend that everyone get the maximum amount of insurance they can afford, so you don't find yourself in a situation like this one.

For vehicle damage, you can bring a $500 dollar mini-tort claim under Michigan law. You cannot sue the wrongdoer driver for more than $500 dollars, unless that driver is uninsured. Your own insurance company is responsible for vehicle damage over and above the $500 if you purchased additional collision coverage, as well as other important No Fault PIP benefits. The wrongdoer's insurance company will only be responsible for your pain and suffering under Michigan's auto accident threshold law. I've included a link you may find helpful on how to easily recover your mini-tort money from the other driver's insurance company here: http://www.michiganautolaw.com/no-fault/mini-tort/index.php

No, you can not. I am saying the same thing as the others but trying to say it simpler. Michigan is a no fault state, which means that your insurance pays for your car (other than up to $500) no matter who is at fault. If you don't have coverage, you sustained an uninsured loss.