You can't just copy the files on to your usb drive as you need to make the usb drive bootable.
However fortunately there is a piece of software called Wintoflash which will copy the Windows files for you and make your flash drive bootable.
Very simple to use software just download it from here
http://wintoflash.com/download/en/
Run it, and point it to where your windows files are and where your usb drive is on a computer with a working DVD drive (nb. you need to copy the windows files from the CD onto the hard disk of the computer your using to create the bootable usb as Wintoflash needs to edit the files a bit and can't do that on the CD).
Accept the EULA and install it on to your USB drive.
Then plug your usb drive into your laptop with the none working drive.
Ensure your BIOS is set up to boot from USB first. If you look in your BIOS it might not boot off USB if you tell it to boot from USB first, this is because some flash drives are treated as hard drives even though their plugged into the USB drive, if this happens tell the computer to boot of the hard disk and in hard disk priority change it to the USB hard disk first, followed by your other hard disk e.g.
Boot Order menu
1. Hard Disk
2. CD-ROM
3. USB
then in hard disk priority section
1. Kingston 1Gb USB drive (or whatever USB drive you have)
2. Seagate 320Gb MA3535 (or whatever hard drive you have).
Of course different BIOS are all different.
When it starts booting off the USB stick you should have a menu that appears first.
By default the second option is selected, on first boot choose the first option to re-install windows otherwise it will just attempt to boot off the hard drive, then when it gets to the first stage of setup and reboots the computer use the second option.
If you know what you are doing properly with Wintoflash you can also make Windows perform an unattended installation with the various options.