Nahh, the HDD shouldn't affect booting off the CD - only drive detection in Windows XP Setup. I reckon that bluescreen was caused by the difference in hardware, because if the hard drive from the other laptop has Windows installed (and hence, all the drivers for that laptop installed), the Toshiba could be loading what it THINKS is the correct drivers and catastrophically bluescreens because they're not compatible with the Toshiba's hardware.
So, here's what I reckon;
The Toshiba has some retarded issue with booting from XP CDs or any sort of CD drive
there may be a way to fix it, maybe not, you might have to assault Toshiba technical support. But what you could do, is install the Toshiba's hard drive into the other laptop. If possible, wipe it and install Windows 7 onto that drive. Then, use the sysprep utility built into Windows (google that, there's a heap of info on it) to "generalise" that installation. "Generalising" wipes most (if not all) laptop-specific information from Windows. Make sure the laptop shuts itself down after it runs through generalising itself, then remove that HDD and install it in the Toshiba. I can't guarantee that it will work, but if it doesn't bluescreen, you then have a fresh copy of Windows installed on your Toshiba. If it runs for a while and THEN bluescreens, then by the sounds of things your diagnosis may be right (Hard drive is bad) or it could be something else; worst case scenario, the laptop's mainboard/motherboard is faulty. In this case, it's probably a case of throw-away-the-laptop-and-buy-a-new-one.
I'm sure Windows XP also has a sysprep utility, but I honestly couldn't tell you how to use it and I don't know if it even does generalisation...
Anyway, good luck, let us know how you go!