i think he said he has an external hdd, not external optical drive. there would be no issue here if he did.
ok, well i can think of one way to go about all this. using the other computer, create a .iso file from your windows 8.1 dvd. there are different programs which can accomplish this. google "creating an iso file" or something. off the top of my head, nero does it. i used to use a couple other programs, but it has been so long since i ripped an iso file i can't remember off the top of my head.
once you have a .iso of your windows 8.1 dvd, you can create a usb boot thumb drive using the windows 7 dvd tool. it will create a copy of windows install that will boot from a usb thumb drive
at that point, you put the usb drive into your custom pc and go into the bios and select to boot from the thumb drive. go through the normal windows install, but when the computer restarts to continue the install from hard drive go back into you bios and select the boot drive you installed windows to as your primary boot device