First thing first, do NOT boot into safe mode. It may seem counter intuitive, but let me explain. The reason explorer is crashing is because a program is loading that forces it to crash. If you boot into safe mode, that program will load much faster, and you will have little to no chance to do what you need to accomplish.
Fixing this problem comes down to one thing: Being able to click really fast. This is what you do. Turn on the computer with it plugged into an Ethernet cable, click start, and launch Windows Defender. If explorer crashes before you are able to do this, try again until you get it. When you succeed, wait for explorer to crash again, since Windows Defender will remain open. When it is responsive, click on the down facing arrow all the way on the right, and choose “Check for updates”. Chances are explorer will crash again. When it becomes responsive, click on the scan down arrow, and choose “Quick Scan”. The scan will start a stop and go scan… at this point you should just walk away since it will probably take a while. If the scan finishes and no problems were found, then make sure that the updates were applied, and then do a “Quick Scan” again. Windows Defender should find the problem(s), so remove them all.
Now to keep yourself protected...
The easiest way to fix any remaining issues is using Malwarebyte's Anti-Malware (Turn off system restore, Download it, update it, do a full scan, and remove everything it finds).
I would also recommend the following programs to make sure that you don't get infected again in the future:
Spybot - Search & Destroy
Avira AntiVir Personal
Spyware Doctor Starter Edition