Having your set calibrated by an ISF trained technician will help the most. HDMI passes a digital signal (unlike component, RCA or S-Video which are analog). You are currently using Component cables which are the high end analog cables. I would suggest using a decent quality set of these and Radio Shack usually has good deals on them. Switching to HDMI shouldn't show much of a difference unless you get your set calibrated by a pro. Put that money towards the calibration.
Decent Component cables shouldn't show much of a difference but a lot of that has to do with factors such as the source feed, length of cables used, size of TV and the settings you have on it.
Don't overspend on cables (i.e. Monster). Decent cables can be had online or from places like Radio Shack for much cheaper. I bought a DVI cable online from Belkin for $12 but Best Buy wanted $65 for a similar one. No difference in quality.
You can find HDTV calibrators through this site: