This video shows how to install Windows 7 (or Windows Vista) from a USB flash drive or USB hard drive. Copy the files to your USB device, use diskpart to make the partition active, and use bootsect to write the bootcode.
Insert the flash drive into the computer and set it to boot from USB (refer to manual) - most newer computers should be able to boot to usb. Install Windows like you normally would from DVD.
This method should also work if your computer has a card reader, such as for SD cards. If anyone tries this with an SD card, let me know if it works!