Hello everybody,
I had problem with my RCT1 Deluxe I bought during the weakend sales on GOG. The game crashed everytime about 5-15 sec after starting it. I've tried every possible compatibility mode and nothing worked. Than I tried it on my other PC and I found that crashes (or problems?) were caused by my antivirus (Avast 7). After turning it off the game seems to run without crashing.
Hope this helps somebody.

That's odd. I run Avast 7 as well (XP Pro SP3 x86) and have had no problems, albeit I don't use the GOG launcher.