Yes you would also have to buy a new motherboard to upgrade to a more modern CPU since yours is so old. You can do some research by going to the Intel site and researching new motherboard socket types and processors and be sure to match the socket type to the processor you are interested in. You would also have to upgrade ram and quite possibly the video card depending on what type of games you want to play.
You can either buy a new computer or build your own which will get you more hardware for the money and you may be able to use your old case, DVD player, power supply but prior research is the key.
First: select a budget for your build/new computer.
Second: select hardware, and features that you want ensuring hardware compatibility
Third: ensure power supply is powerful enough to run all your modern hardware, Newer higher end cards require a 500 W+ power supply. Most store bought computers also contain a low rated cheap power supply.
Fourth: Keep posting as you choose hardware/features of your own build or pre-built computer so other members can advise on whether items/computer chosen match your needs, are a good deal and most of all compatible.