Using an external hard drive?

You CAN use an external hard drive to boot. However, it depends on if your BIOS supports USB booting (Most BIOSes nowadays do). If it does, then just plug in a USB hard drive and install Windows to it. Because it is USB, though, it will be much slower than an internal hard drive. I would just go ahead and replace the internal hard drive. It should be relatively simple, and not prohibitively expensive.