new Plasma TV, new HTPC build possibility?

so I just bought a 50inch samsung plasma, PN50B650.

I have some parts layin' around from an old computer build...
HD3870
ABIT IP35E
Intel E2160
2Gb (1gb x2) XMS2 RAM

Items needed...
BLU-RAY Player
HDD
Case/PSU
SoundCard??

QUESTION (Just gave info above, dont think you need to know it to answer question)

If I connect my hypothetical PC to my samsung plasma... will I be able to get full 1080P??? or will the connection be downgraded to a 1080i or lower resolution??? The video card has no HDMI option... only a converter from DVI to Component...

******THE WHOLE POINT OF THIS IS COST EFFECTIVENESS*****
If I buy the parts I need listed above, I should be able to complete my PC for under 300.00... If I am to buy a stand alone blu-ray player, I will go for nothing short of a PS3, which is the same cost...

bottom line is, I would rather have a functional HTPC then a PS3 but only if I am not sacrificing video quality...