A user posted this in the forum who had a P50.

Turned NIC (Integrated Network Interface Controller) off and then booted off of USB. Was NOT an issue with any Linux distro just a quirk of the laptop. Am now running 13.10 daily and everything works. Also had to stick with EFI boot ON, Secure Boot disabled. Wouldn't boot off of any media or HDD when mode set to CSM.

http://ubuntuforums.org/showthread.php?t=2163854

Another user with P75

Toshiba Satellite P75 intel hd 4600 needed both:

acpi_osi=Linux acpi_backlight=vendor

The Easy Way

The easy way to do what you want is to not boot the 32-bit Ubuntu directly; instead, install it in a virtual machine (in VirtualBox, QEMU, or VMware, for instance). Depending on your exact needs, this may be all you need, and it's a lot easier than trying to get everything properly multi-booting. OTOH, if you're developing, say, drivers for your computer's hardware, a virtual machine will probably not do what you want.

The Hard Way

Broadly speaking, I can think of three ways to do what you want (aside from the easy solution of using a virtual machine):

• Go 100% BIOS/CSM/legacy -- You can wipe the computer and install all your OSes using the Compatibility Support Module (CSM), which enables BIOS-mode boot loaders to work. This will make it much like installing on a computer from several years ago. The trick is that it can be hard to control the boot mode of installation media, particularly if you're unfamiliar with the tools and techniques used to do so. See my Web page on the subject for more information; however, that page is written with an eye towards discouraging mixed-mode installation, so information on doing a 100% BIOS-mode setup is kind of buried amidst other things. Also, if you want to keep Windows, you'll need to jump through some exotic hoops or re-install it completely, and to do the latter you'll need to track down appropriate installation media.
• Use a 64-bit EFI-mode GRUB to launch a 32-bit kernel -- The 64-bit EFI-mode GRUB 2 can launch 32-bit Linux kernels -- or at least, some of them can. (GRUB binaries vary significantly in how they're built, so I can't promise that all 64-bit EFI-mode GRUB binaries will do the job.) As a practical matter, to work in this way, you'd probably want to install Windows, then a 32-bit Ubuntu (in BIOS mode will work fine), then the 64-bit Ubuntu in EFI mode. Ideally, the 64-bit Ubuntu's GRUB should detect the 32-bit Ubuntu installation and create separate menu entries for it. They might not be well-labeled, but they should work. If they aren't detected, it might be possible to create entries manually.
• Use rEFInd to boot 64-bit EFI-mode OSes and your 32-bit BIOS-mode OS -- This approach is similar to the preceding one; however, you would install my rEFInd boot manager after completing the 64-bit Ubuntu installation. You would then edit /boot/efi/EFI/refind/refind.conf: Uncomment the scanfor line and ensure that hdbios is among the options. The result is that rEFInd will enable you to launch Windows or 64-bit Ubuntu in EFI mode, and it will show a gray diamond-shaped icon that will launch the BIOS-mode GRUB from the 32-bit Ubuntu installation. This GRUB will in turn launch the 32-bit Ubuntu. (It may eventually pick up and show options to launch the 64-bit Ubuntu in BIOS mode, too.)

In theory, any of these options should work. In practice, they all present pitfalls during setup, and any might be blocked by firmware quirks or other problems. Thus, you may need to try two or even all three of them before you get something to work.