I think a little more detail might help but I will give it a shot.
What Breed says about needing better cable might be true. The current Standard is RG6 whereas your rig may have the old RG59. But.....try it with the old cable first. Shorter runs may work fine. Satellite LNB's are powered by your cable box so longer runs of RG59 can cause problems for your Digital Boxes but when we are talking short runs (say 10-15 ft), then it isn't so much of a problem. The longer the run, the greater the loss of power and the harder your digital box has to work.
Now onto other things. If you have some kind of digital box with a built in PVR, you should be able to ditch the splitters.
You will need to use HDMI cables most likely to connect things to your TV. Things being your Blue Ray and your PVR.
I will assume your new TV has more than 1 HDMI input on the TV.
So, cable from satellite goes to your Decoder/PVR
Decoder/PVR goes to TV via HDMI
Blue Ray Player goes to TV via 2nd HDMI
If you are using an Antenna, you will still have one of these decoder boxes. Some may not have an HDMI out on them. If so you will likely have to use the old composite cable (the yellow, red and white cable) to connect to your new TV. It will likely still have those inputs on the back of the TV.
1999 - National Tropi Cal