My first point of advice would be to actually buy the game in question. Whether its giving the starving video game artists a break or depositing money straight in Steve Ballmer's pocket, however you look at it this is the easiest and most legal solution.
If that fails due to an empty wallet or not listening to your conscience, I would start by trying a Google search for what's called a no-cd patch. They're nifty little gadgets that trick an application into thinking the CD is already in the drive. You won't even need to mount the virtual disc you illegally downloaded. These also work for games you've actually bought, if you ever venture into your local Apple Store or Best Buy instead of browsing the Pirate Bay.
As no-cd patches are in a legal grey area I'm pretty sure I would be reprimanded for advising any specific sites, but a Google search should turn up tons of seedy destinations that will provide you with the fix you need. However, many of the sites I've come across are malware-plagued, and the patches themselves are rather unreliable. How to install the said patch really varies by program and I can't give any more specific advice on that.
As far as mounting the CD via Toast/Alcohol, it likely wouldn't make a difference. Besides, your Mac already mounted the disk image. That's how you installed it. A third-party program that would do the same thing Leopard does is unlikely to make any difference. I mean, you could try it, and if it works, more power to you, but to me it seems more likely that one of the above methods would work better, mainly the first.
Really the overarching theme here is to just buy the game. It'll solve all of your disc-related problems instantly, not to mention potentially saving you millions of dollars in legal fees later on.