Could I use one computer to connect to another one to reinstall the operating system and hopfully fix it

Generally speaking, no.

There are certain instances in which you can do this... but they include things like having a remote KVM (or HP's nifty iLO that they have on servers), and some way to boot the PC to a network controller using PXE with a server that has the OS files on it, or if the computer you need to reinstall the OS on is a virtual machine.

But generally speaking, no, you cannot reinstall the OS on a computer remotely.

Why can't you use the main PC?