Let's see... how do I explain this?

No, if you use a 32-bit operating system you can’t use more than 4 GiB of RAM.

Period.

With 32 bits you can only reach 2 to the 32nd possible addresses. There are mechanisms proposed for accessing addresses above 4 GiB, but they have their problems. (When the world was young and we used the 286, there was a little trick for using memory by segments, but that really was a headache, something similar to what PAE does).
In any case, this is “virtual access” to more than 4GiB, achieved with 4 additional bits of indirection; at any given moment, the CPU only accesses 4GiB.

Either way, PAE mode creates plenty of inconveniences, so it’s not a real solution to the problem.

Other systems support PAE, but I insist, you are always reaching the extra memory indirectly. It’s better to go with a 64-bit system, because it will give you fewer headaches and won’t degrade performance.

And this is not a Windows limitation. You won’t be able to do it with (32-bit) Linux either, no matter what the Taliban tell you.

If you want to use more than 4GiB of RAM you need a 64-bit processor and a 64-bit operating system.

I recommend reading this Kriptópolis article on the subject (oh! and Bill Gates never said that 640 Kb of RAM was enough)