How can your motherboard NOT support more than 3Gb? Do you actually know anything about building computers? Even if there are two memory slots (and, why would you buy a motherboard with only two slots anyway), you can take the old RAM OUT and put new RAM IN. Chances are, if the computer is less than 6 years old, each slot will support at least 4Gb in each slot. If your computer is older than that, well, buy a $300 PC and you'll be thanking me.
For the record, you can buy 8Gb of ram for $30.