Pointless Mac vs. PC arguments aside, there's not much to tell you other than saying "I get a computer I want to work on, or you get somebody else to do the job." That's certainly what I'd say, particularly if I wasn't getting paid properly for the work. Sounds like maybe this is an internship of some sort (I hope so, if it's unpaid work)? If so, that's about all you can really do.
If you do want to try to make an argument, there's only three that might get you anywhere:
1) Spec out a Dell that costs the same or a bit more than the G5 (not hard, obviously; doesn't matter if it's quite equivalent or not, or if there are cheaper options available). Then tell the boss-type that this is the Dell you'd need to do your work, but the G5 is cheaper and you'd be more productive and happier on it.
2) Settle for a much cheaper Mac--an eMac or laptop--that's in the same price range as the Dell in question.
3) Tell him you'll work much more efficiently on the Mac (which I certainly hope is true, or you SHOULD be getting a Dell... er, let's say IBM), and it has the tools that you'll need to get your job done effectively. I'm assuming this is the truth
There is actually a huge 4th argument, and that would be VirtualPC, but that won't run on the G5 you want untill MS can get VPC7 out the door this fall. The advantage of VPC is you can have multiple versions of Windows running simultaneously, each with a different configuration (most importantly IE5 on one and IE6 on another), in addition to Mac-native versions of Opera, Mozilla, and Safari. This lets you test markup on a complete range of browsers without having to install multiple OSes on the Windows machine you'd be working on, and having to bother with restarts every time you wanted to test someting.
If the project is long enough, then maybe that'll still be a good enough argument (by the time it ships in the Fall, you'll be ready to use it), but that's assuming that MS actually meets a constantly-slipping ship date.