Trinity is the name of the collection of all of the Sins games. It's exactly the same content-wise as having all three games, and is completely compatible in multiplayer. You're not missing out on anything.
It's possible you have a bad disc. If you have a bad disc, you may be able to take it back to where you purchased it and swap it out for a good one. Your other option is to use Impulse to download and install the game:
http://www.impulsedriven.com/impulse_setup_full.exe
Once it's installed, you can log in using your forum account. To register the game with your account, click on the help icon in the upper right of the Impulse interface (the one that looks like a blue circle with a question mark) and select "Register a product with Impulse". Once on the registrations page, in the bottom right, click the 'Add Registration' button. In the Window that appears, enter your serial number (Remember all serials use letters A-F and numbers 0-9. Dashes in the serial number are important and must be included), followed by your e-mail you used to create your forum account, the product category and the product name (If you serial is recognized, these last 2 will be auto filled). Click 'Add Registration' button and you've registered your product. This will register the software to your account, and get you the latest updates to your product, as well as keep track of the serial number if you ever need to install again.
