RAM upgrading is really quite painless. You wouldn't add ram to your current setup, you would remove the old ram and replace it with new DIMMS of a higher capacity. By removing the old memory not having any free memory slots becomes a non-issue. A PC bought circa-2003 should use DDR ram.
There are two options for a RAM upgrade, depending on what your PC supports.
The first is a 2GB upgrade, with 2x 1GB DIMMS. Something like this.
The option, if your system doesn't support 1GB DIMMS, is a 1GB memory upgrade with 2x 512MB DIMMS. Something like this.
The prices are very reasonable, and you could even get a few dollars for your current ram if you were to sell it on eBay. You could also possibly upgrade with 4x 512MB DIMMS, but without knowing the specific model of your PC I don't know how many DIMM slots you support. It's fairly unlikely for a PC from 2003, but if your PC uses either RDRAM or SDRAM I wouldn't bother with any sort of an upgrade. The RAM in these cases is too expensive to buy in any sort of a decent capacity to make it worthwhile.
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