Hi bigrobot,
Sort of possible, I think, but not simple. You can boot from the network if the other laptop is set up to serve the boot image. There are probably better ways to achieve this, but one that I know of is how the LTSP thin client software does it (see
http://www.ltsp.org/documentation/lt...-4.1-1-en.html ). LTSP explains in detail what steps it goes through to perform a network boot, though as it is for thin clients it won't be ideal for your purposes.
For all this to work, you need to get your problem laptop to look on the network for a boot device. Look at chapter 3 in the page I linked to - it explains the different client boot methods.