Can my PC handle more RAM?

Haha, surely it's up to you to make the choice!
If your motherboard box has a Compatible with Windows Vista/7 sticker on it, it means it can run both 32-bit and 64-bit.
64-bit has backward-compatibility to an extent with 32-bit.
To be sure, to check for compatibility, here you go: MS Compatibility Assistant.
Just search for you mobo and see if it's compatible.

Well, in case you change your mind, feel free to post a thread and PM the link.
You'll be better-off/safer with guidance of experienced TS members!

I couldn't find my Motherboard on that website, but I'll check for a sticker on my Motherboard once I get past my lazyness!

Looking at the manufacturers pages for your motherboard, there are several clues pointing to the fact your motherboard was designed for 32-bit and 64-bit operating systems.

• Clue 1 - Memory noted in red stating that only 4GB will be usable with a 32-bit operating system.
• Clue 2 - Looking at driver downloads there are both 32-bit and 64-bit versions of XP, Server 2003, and Vista.
• Clue 3 - 64-bit CPU's listed in the support list.

On a final note:

Windows 7 may not have the motherboard listed as being supported. However there are Vista drivers available for your motherboard. You can use Windows Vista drivers if there is not Windows 7 drivers available. Just remember to match the driver bit version with the operating systems bit version (64-bit drivers for 64-bit OS).

I'm just going to save you a lot of time and tell you flat out that your motherboard is x64 capable and should have no issues running Win7 x64.

Your mobos bios/manual update pack

So... What exactly do I do now?

Decide whether you want a 64-bit operating system, which will be capable of using all 4GB of system memory.

Windows 7 has been know to install drivers for much much older hardware than you are currently using. As I stated earlier, there is not much difference between windows 7 and Windows Vista. Windows Vista drivers have always worked as a substitute when Windows 7 drivers were not available.

Gawn dangit, I keep forgeting about tech spot threads and don't reply for ages, sorry all.

So now that we've agreed that my PC is compatible with a 64-bit OS, I would like to convert to a 64-bit OS. What is the next step?

To begin with, you can't really "convert" or upgrade to a 64-bit OS. You always have to make fresh install.
Back up all your data first.
You must have a copy of a 64-bit OS at hand. Do you have a 64-bit version of Windows 7? If not, would you purchase it or use another 64-bit OS such as Ubuntu?

I don't mind loosing my current data since I don't have anything important on my PC, if necessary I can head to the PC store and buy a disk to back up my data. If a Windows 7 OS isn't too expensive I'll go ahead and buy a disk. If you could be so kind as to leave me some simple instructions on how to back up my data and install the OS, I can do it when I'm ready and don't have to dig up this thread after a couple of weeks again to ask how to do it.

Here you go:

Backup:
Couldn't be simpler than copying all the files (the data to be backed) to a different storage device, say an external HDD.

OS Installation
Simply reboot with the 64-bit installation disk in the CD tray (and set as the first boot device in the BIOS, obviously). Follow the on-screen instructions and select the partitioning system as you want. A "Clean Install" is your only option there.