I'm not sure this will work for everyone, but it worked very well for me. Now happily playing Final Fantasy 7:D
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Specs.
pIII 600mhz
512mb Ram
9550 Sapphire Radeon 128mb
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Now to address the problem...
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Problem: Starting up the game, there is a black screen and no sound. Pressing buttons makes us go to the Continue/New Game screen.
Solution: Installed fresh(Do NOT install DirectShow drivers), applied 1.02 patch http://rpghaven.uni.cc/goldfinger/ff7/ff7102zx.zip, appplied upside down movie patch http://rpghaven.uni.cc/goldfinger/ff7/ff7betap1.exe, and for later on in the game, just incase the game freezes on the chocobo races, applied the chocobo patch http://rpghaven.uni.cc/goldfinger/ff7/ff7_chocobo_patch.zip
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Well, i hope this helped you, and if it did not, feel free to e-mail mne at Gamergod.Gold@gmail.com with the subject Final Fantasy VII or something along the lines of that.
(NOTE: these files are all on my server, are guaranteed to work forat least 5 months after posting this.)