ok, a little googling helped me understand what you are doing. more context would have helped a lot. p80p is an onboard diagnostic 2 digit LED display driven by the bios (POST code, I dunno). I assume that you are planning to take the p80p pins and connect them to the display. what motherboard are you using?
so, that said, your diagram is wrong. you don't connect the display to voltage or gnd. the segment pins (or hidig/lodig) have all the driving voltage. forget the floppy cable. Hidig and lodig are the common pins for the coresponding digit. the segA-G will be connected to the same segment on both digits. the BIOS (or ?) will select the digit via the hidig/lodig pin and then power the desired segments. it will alternate rapidly between the two digits so they will both appear to be illuminated at the same time.
You need to understand whether the p80p port expects a common cathode or common anode display. do you have an actual 2 digit display in hand?? can you point to where you are getting this information?
I think, from what i read, that the p80p is driven with 3.3V. so you will need to calculate the resistors based on that and forward voltage of the display segments. this will be in the datasheet. If you don't have a datasheet, for red, use 2V and green or yellow, use 2.2V. the resistor is used to limit the current. I'd probably pick 20 mA. the resistor is calculated via the formula R = Vf/I = (for red) (3.3-2)/.02 = 1.3/.02 = 260. choose the next higher standard value resistor. 270 will be fine for red. don't use blue LEDs - they require more than 3.3V. note also that some super bright leds take higher voltage and/or current. I'd would not use them here since the current capacity of the p80p circuits isn't clear.
also, next time try using a title that is discriptive of the problem, not the poster.