You also won't be able to install it from the desktop because the drivers that windows would install are associated with the system you install it on. So windows would think you are installing it on the desktop so all drivers and registry items would be written for the desktop. So when you plugged it into the laptop you'd still get a boot error.
1. You could order a new CD ROM drive.
2. You could use the recovery partition to put the computer back to the original state. Most laptops today come with a small 5 to 10 gig partition that if you boot to it, will reinstall the operating system and any programs that came with the PC. Essentially the computer will go back to it's out-of-the-box state.
3. You could install XP from a network drive (google this, there are tons of articles on it)