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I need BIOS support for more than 4GB RAM...

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As you are running the 32-bit version of Windows 7, even PAE will not get you past the 4GB limitation.

"Microsoft Windows implements PAE if booted with the appropriate option, but current 32-bit desktop editions enforce the physical address space within 4GB even in PAE mode. According to Geoff Chappell, Microsoft limits 32-bit versions of Windows to 4GB due to a licensing restriction[2], and Microsoft Technical Fellow Mark Russinovich says that some drivers were found to be unstable when encountering physical addresses above 4GB.[3]. Unofficial kernel patches for Windows Vista 32-bit are available[dubious ? discuss] that break this enforced limitation, though the stability is not guaranteed."

Even if you could get past the 3GB limitation with a BIOS change, the physical hardware in the chip-set and system board is still very apt to limit the amount of installed RAM that will work.

Now, the reason why Toshiba (wisely) limits the system to 3GB of installed RAM is that the extra 1GB of upper memory basically draws power but is not usable by Windows.

As Colin stated, many chip-sets do not have the hardware implemented to support more than the full 4 GB of addressable RAM even if you could invoke PAE mode.

That upper 1GB is where the physical addresses for your video card, system bus and system devices resides. It's not just the BIOS that would need to be revised to have access to more than the 3GB of RAM that Toshiba limits you to. You would need to restructure how the physical address lines are routed on the system board.

Your options to improve performance of memory intensive applications include:

Set virtual memory to a minimum of 2X installed RAM with no maximum.

Use a fast USB flash drive as a ready-boost device.

Limit the number of applications that run and load at startup.

Still, the best way to resolve the memory limit for 32 bit versions of Windows is one you excluded. Move to new hardware with full 64 bit support.