Did you do as suggested by Bobusboy, and run the upgrade advisor? It will let you know if your hardware is compatible with windows 7. It will also inform you if the current set of software installed is usable with windows 7. If it is not then upgrades or alternatives are normally available. The important factor here is usually the hardware. That is the first place to start. It is free and will give insight to your next direction. If the hardware is all compatible then go ahead and spend the 25 to 50 dollars to upgrade the RAM and install windows 7. If you want to save any installed apps and settings there are different ways to go about that. If you can backup the data and reinstall the apps, that is always your best bet.
One of the easiest ways to perform an inplace upgrade to windows 7 is to first upgrade to Vista,(eew) then upgrade from there to windows 7. Xp is not readily upgradeable to windows 7. Since it on the same machine you cannot use the easy transfer method directly. Acronis and VMware both have software that can be used to virtualize the current running OS installation, then boot that into a VM and then use the Easy transfer wizard. I may be getting to deep or advanced for what you are hoping to do, but just know there are always options.
If hardware is not compatible with Windows 7, but you still really want to run windows 7 on this computer, you resort is to install a light-weight linux distro, such as Xubuntu (there are many others) and install Virtualbox from Oracle (Sun Microsystems), or better yet, VMware (Vmware workstation is free to try- create the vm, then install free vmware player run it) create a VM in there that will run Windows 7. The linux will normally (99.9%) utilize all your hardware and then make it available for the VM to use. If the linux is used as a hardware "translator" and the VM is run in full screen mode, the operation of windows 7 will be seamless.
A couple gig of memory is definitely less expensive than a new computer. So If I was needing to save some money, but really wanted to have Windows 7 running on incompatible hardware, I'd make use of the VM