Although it is possible for you to buy a DVD player that decodes Dolby Digital and dts, and then use your current system for the front right and left channels, add a subwoofer and add amplifiers and speakers for the other channels, I advise you to take the advice of the others and plan on just buying a new surround receiver. If you have room for it, put your current stereo in another room in which you would enjoy listening to music, and use the new surround receiver in the room with your TV.
And, as Exit says, pick your new speakers first, and then select your new receiver (or separates, if you have plenty of money and wish to go that route). My advice is to budget most of your money on the speakers (including subwoofer), as they affect the sound far more than most other components. Listen before you buy, and listen to as many speakers as you can stand to listen to.
Also, you will want to make sure that your front three speakers are "matched", so that sounds that pan across the front do not change tonal quality when moving from the left to the center to the right. Ideally, the front three speakers will be identical, but for space and aesthetic considerations, many people use a horizontal speaker designed to go with whatever right and left speakers they select. I personally use a "bookshelf" speaker in the middle that is exactly like the front right and left speakers, and therefore I have perfect voice matching across the front.
Then, select a receiver that does everything you want it to do, and that can deal with the speakers you have selected (or add power amps, in the event of selecting speakers that are very low efficiency or a difficult impedance—this is why you select your speakers first, so you will know what kind of amplification you will need for them).