Raggaie - Here is a primer on connections. I can add more later if you have need. First, let me set out the resolution capability of each connector from worst to best (currently available in the mainstream). I will point out the downside only. Technical jargon is available if you really want to read about it. This will help you understand your current connections.
1. Coax - This is the input from your wall usually. Coax (F-pin connector) cable carries the audio and video on a single cable. Generally ok in short lengths as long as it is properly insulated and the cable's specs are sufficient to carry the signal. RG6 is generally accepted as the standard. If you have RG59 pull it out as it will not carry HD. You need at least 2Ghz for HD. Your display device will up-sample the incoming signal to 480p, or perhaps something higher (depends upon the capability of your sets internals and your settings).
2. RCA – A single yellow cable connector. Not much better than Coax. The main difference is that it separates the audio and video by using the red/white (or red/blue) analog cables to carry the audio. This assumes that all three connectors are present. Same up-sampling issue as noted in #1 above.
3. S-video - better than #s 1 & 2, but only because the cable splits the color and black and white signals. (Luminance and Chrominance). Audio must be carried on separate analog cables.
4. Component (a/k/a RGB) - Three cables combined into one unit. Purpose is to split the red, green and blue colors. The display device puts the signal back together. Component is an excellent way to go with progressive scan DVD players. Keep in mind that you lose some resolution (softening of the picture) going this route because the signal from the DVD is in the digital domain in the box. That signal is converted by the DVD player's DAC to analog before being fed to the component output. The signal travels the length of the component cables in analog before being converted again to digital (ADC) by the set. Depending upon your set, and its capabilities - up-sampling etc, you may have yet another conversion back to analog before you see what is on the display. Unfortunately there is not much you can do about this process without purchasing an expensive video processor. If you are happy with the signal then that is all that matters.
5. RGB/HV - rare. Mitsubishi's sets had this connection for a while. Basically it is RGB + H (horizontal) and V (vertical). The added connectors are generally yellow and white. Better than RGB, but still analog.
6. DVI- (comes in three flavors - DVI-A, DVI-D & DVI-I). You most likely will see DVI-D (digital) and DVI-I (analog and digital) on today's consumer sets. This connector will carry digital video signals, but will not carry audio. Some DVI cables are limited in bandwidth and will not carry 1080i at long lengths. Keep in mind that "long length" may be anything over 10 feet. DVI is on the way out, so I would not worry about it unless your set happens to have a DVI connection port.
7. HDMI - The newest connection format. HDMI is still in its early days, and can be confusing even to the experts (a club that I don't belong to). HDMI was created as a single cable solution for carrying video, audio, and command signals from one component to another. Like IEEE (a/k/a firewire) the components are supposed to "shake hands," tell each other about themselves and provide a pristine viewing experience. Sadly, it has not worked out as intended. The standards continue to evolve. Early HDMI could not shake hands, and when it did it did a poor job. That said, HDMI is the future. We should see incremental changes - for the better - over the next several years. Many of the newer systems are backwards compatible to fit into older (older in this case is anything more than a year old) systems. The downside for now is that the newer display devices with HDMI 2.0 and above cannot bring older devices up to the current standard. Your system is only as good as the weakest link.
7. HDCP - This is not a connector, but a standard for encrypting the signal. I add it because in order to resolve true 1080p (and in some cases 720p and 1080i) your source device (sat. box, dvd player etc.) will "talk" to the display device to confirm that the display device is HDCP (High Definition Content Protection) compliant. If not, you will get a downrezed signal (perhaps as low as 480p).
My advice - 1. you can keep your connections as they are and use the hdmi connection for the new Dish receiver. Just make sure that you reset the output on the Dish receiver to take advantage of hdmi. Dish may have changed this but for a very long time, in order to switch the inputs you had to start off in S-vid or coax. If the Dish dude is hooking you up he can do this for you. I would not use the S-vid for the DVD player. If anything, I might be tempted to use the S-vid for the X-box.
2. You can purchase a hdmi switcher. This will give you more hdmi ports for future source components. Most new DVD players have hdmi connectors. You will want to use it if you can. Remember the discussion on DAC & ADC from above? You can avoid the multiple conversions going with a switcher.
I do hope that this helps. Kirk