The cable you first described with the Red yellow and white colors is a composite cable, and you are correct in noting that upgrading to a HDMI cable will actually produce a much better picture. When you change from a analog cable like composite to a digital cable like HDMI, you have to change the settings in the Blu-ray Player to reflect the output signal.
One of the first things you will want to check is that you have an HDMI cable that is v. 1.3.
In the settings menu of the Blu-ray Player, you'll be able to choose which ouput you would like to use. I would recommend setting this up while the television is hooked up with a composite cable. After you change the settings, turn off the unit and attach it to the television with HDMI. You do not want to have both cables hooked up at the same time.
Keep me posted.
I recently aquired a 40-inch 530 LCD and a P1620 to go with it. The BD player included a red-yellow-white component cable, with which I was able to hook up the player to the TV, having fairly good picture and sound.
My troubles started when I got a HDMI cable in the hopes of using this to attach the two. After removing the component cable and installing the HDMI one I entered the setup menu on the TV and it autodetected the player as "Anynet BD". However, switching over to the HDMI source resulted in the screen blinking between black with a "no signal" message and the distorted blue screen of the BD player with snow on it, while in the top left there it displays "720 X 480 @ 60 hz".
Resetting the TV to factory settings and attempting to auto-detect again yielded no improvement. Attempt to switch back to the component cable resulted in the screen blinking between the blue screen of the BD (without snow this time) and a black screen with the "no signal" message. Needless to say, it is quite frustrating that the HDMI connection does not work, and neither does the previously functional component connection. I have of course checked the various cables and they all appear to be in order. Any advice would be appreciated.