32 bit versions of Windows are limited for marketing purposes. The operating system is perfectly capable of handling more than 4GB of physical memory thanks to the inclusion of Physical Address Extension (PAE) but applications that are not PAE aware will be unable to address a virtual address space greater than 4GB.
There are several solutions available:
1. Install the consumer preview of Windows 8 and use it for free. Please note that application support is still immature. I am not sure how long the consumer preview will be available for but it may be around until the official release of Windows 8.
2. Install a patch which enables the remapping of RAM in 32bit consumer versions of Windows Vista and Windows 7 (Server versions have this enabled by default). This will allow Windows to use the entire 4GB of RAM that you have right now and also will allow you to install more. Please keep in mind that some driver compatibility issues have been reported.
3. Download and Install Windows 7. You can use it for free without a licence key for 30 days. After the 30 day trial has expired you can rearm it 3 more times for a total trial duration of 120 days. After this you must purchase or remove the software.
You can get the trial download here:
http://en.community.dell.com/support-forums/software-os/w/microsoft_os/3316.2-1-microsoft-windows-7-official-iso-download-links-digital-river.aspx
If you go with option 1 or 3 you will have to wipe your hard drive and start over fresh.