would using a TFP401A doe the DVI input and then putting it into an SN75LVDS83B to give the LVDS output to the screen?
You would be dealing with about 750 MHz signal on the DVI TMDS lines, so you will need to very careful with signal integrity, meaning you must maintain consistent impedances, and make sure you have low interpair skew (all differential pairs must be the same length), low intrapair skew (both conductors of each pair, usually twisted together, must be the same length), low crosstalk (minimize coupling of signals between the TMDS pairs), and maintain the TMDS eye (control impedance, and especially control capacitance of each pair), all per the DVI spec. Not trivial, and is generally difficult to maintain if you're doing hand wiring/breadboarding/hacking. And that's just for DVI; I don't even know about the rest of the signal paths.