hi jeniflen!
There really is no reason to throw out that system, now that you have provided some more information about it.
It has a good socket, good memory and even a PCI-Express slot for adding better graphics/3d card. It will take even the most current Intel Extreme Edition Pentium processors and dual-core processors. It also has dual-channel memory support and many features.
You can likely play Sims2 right now, but extremely, extremely slowly. All you'd have to do are some downloads and driver updates, but you really want at the very minimum would be more memory. The ideal would be more memory and a new 3d graphics card. This will then beg how big of a power supply your system has, which we may still need to determine.
To try things right, now- first thing you should do is update the drivers for your current Intel integrated card, then update directX.
To do this, start with the videocard drivers at:
http://downloadfinder.intel.com/scr...&OSFullName=Windows* XP Home Edition&lang=eng
Click on the DOWNLOAD button on the above link. Install these drivers and you'll likely need a reboot after wards.
Then, update your directx to the latest 9.0c version at:
http://www.microsoft.com/directx
Click the "Get the latest version of directx" link at that page and download/install this.
You should be able to get Sims2 to install and work, but it will be excruciatingly slow as you have too little memory to run this game and XP, not to mention your integrated videocard also takes some of your system's memory.
That motherboard of yours takes DDR-400 memory, you can add 1 gig of dual-channel ddr-400 memory cheaply and it is very easy to install.
2x512mb sticks to retain dual-channel memory can be added for $109
http://www.newegg.com/Product/Product.asp?Item=N82E16820148007
A new PCI-Express videocard that would be perfect for Sims2 would run you about $80-$120 and there are many to choose from in that price range.
If your power supply doesn't have enough power for these upgrades, a new power supply will be around $50-$100. Unless you know the exact model of E-Machines you have, the only way to check your current power supply is to open the case and look at the sticker on the power supply itself.
All being told, you should have everything you need for playing Sims2 for under $200 US through upgrades on your system. You should be able to install the memory yourself, as well as the videocard, as it simply requires opening the case, snapping in the memory into locking slots, and screwing down the new videocard. There are some settings and driver installs that can get tricky, but the members of this forum are here to help you with that should you encounter problems.