Maximum usable memory for 32-bit Win 7

No you won't be able to use more than 3.0-3.25GB of RAM in Windows7 x32 depending on your MB

Use X64 instead

Memory re-mapping only has an affect on 64 bit.

I took a look at Task Manager, and it also shows 2048 MB as available memory. Looking at the videocard's specs, I can see that it has 1024 MB of dedicated video memory, and shared system memory 767 MB.

Don't try adding or subtracting this from anything as it is only used if the video card runs out of memory, until then it is only allocated (cached) and free for use by anything that needs it.

Knowing that the maximum memory 32-bit Win is able to map is 4 GB, still the math doesn't seem to work for me. 2 GB for OS + 1 GB for the video adapter makes a total of 3 GB. If the shared memory isn't in the 2 GB Windows 7 shows as available, then we'd have 2 GB + 1 GB + 0,7 GB = 3,7 GB which starts to sound more reasonable.

For fact, I know that I have memory re-mapping on in BIOS, and BIOS check says 4096 MB of memory installed. The motherboard in question is ASUS P5B. Should I somehow be able to get Windows to use 3 GB of the 4 GBs installed, or is the latter math part right, and the system is already using all that it can?

More like totally wrong. It should be 4 GB - 1 GB for the video card - everything else that needs to be mapped = whatever is left. In your case you went from a video card with 256 MB when combined with everything else that needed address apce and had ~3 GB useable, to a card with 1 GB so you're starting at 3 GB left before everything else is addressed; and not going to try and figure out how it worked out to another 1 GB addressed.

As yowanvista said, you want to use 4 GB go with 64 bit Windows.

Try device manager and show hidden devices to see if you old graphics card is listed. Uninstall it if so and reboot.