SO I signed up to gog just to download this game because I had it when I was smaller and love it soooo much. I buy the game had some trouble installing it (my fault) and then it's installed and it says I only have a 1 hour trail and then I have to buy the game off another site for $19.95. I don't know if this is how gog runs or what, do i have to pay for it on the other site? also to site doesn't look very safe... like I would get a virus from it.... The site is called Download free games.com don't know what is going on but if I did pay $10 for a 1hour trail I'm kinda going to be upset.

Games you buy on GOG you download from GOG. Don't visit another site.
The Installer should have an orange Icon with a white disk on it and a file size of 375.251.981 bytes (You can check it by right clicking on the file)

It seems you caught malware. If you are lucky it only wants to lead you to that suspicious site and pay there, but usually malware comes rarely alone. Best thing to to would be to reinstall windows, but thats a huge task. At least grab a good Antivirus and let it run over your whole disk. Maybe take a look at the 30-Day free trial of Geek Budy you get with Comodos Antivirus suite http://www.comodo.com/home/internet-security/free-internet-security.php

To obtain the installer from gog.com, supposed your money went there and you didn't pay on the wrong site, do the folowing:
Log in to your account, then visit this URL https://secure.gog.com/downlink/game2/rollercoaster_tycoon_deluxe/1_installer_0
Note the https and the subdomain "secure" of gog, only there you get your games.
If you click on your account name after logging in and clicking on the Rollercoaster shell in your gameshelf, you should see the same link appearing named "Windows Installer"

Ok I re-downloaded it from gog by clicking on the "Windows Installer" and I got the Orange Icon with the white disk on on it, I click on it and it runs an authentication check and then it dose nothing...... I don't understand why I am having so much trouble.... :(

You've definitely got malware. Anything you buy from GOG is yours to download and play as often as you please. There's absolutely no paying for hour long trials or any of that nonsense.

Perhaps you should get Malwarebytes and let it give your system a good once-over. Just make sure you download it on a PC you know is clean and run it on yours from a USB stick, just to make sure the malware doesn't get a chance to neuter it.

Hope that helps.