Better later than never?
I don't know if you're still having an issue, but for what it's worth, I also had HUGE problems with RCT3 from the minute I installed the game. It was slow to begin with but once I put in about 15 rides, it would 'stutter' and eventually just freeze up.
So, I quit the game and restarted. From the game's main menu, I went into Options and dialed back most of the GUI settings. Once my park loaded, I immediately went into the 'View' options and toggled off the ride supports; that helped a BUNCH.
I just bought & installed 'Soaked' and before playing, I double-checked the GUI settings and dialed back the water refraction, etc. The game is back to 'normal' and I'm very pleased - it's actually running quite fast. I moved to an iMac from a
very strong PC and the iMac's game play is now equal to my old machine.
Dial back your GUI settings and get 'Soaked.' I installed RCT3 only about 2 months ago and just got Soaked, so I missed the original RCT3 patch. Thus, I can't say if that patch would resolve your problems or not - but cutting down on the GUI display helped tremendously.
I hope this helps - or that you found resolution in the meantime!
Now we need Aspire to include the Forbidden Tomb scenery in Soaked
(!) AND to release the Wild! expansion.