Woah. Before you go down this route I feel inclined to ask what exactly you're trying to achieve here?
The reason for building one seems to be based on entirely this:
I figure if they can do wonders with lot's of people's personal computers, they'd probably salivate at the mouth for a full-fledged mainframe.
The reason I ask is because what exactly you want this to work for will depend on how you tackle it. If you're mainly after parallel number crunching then you may well find a single PC, or 2-3 PCs with Semprons and 4 HD6990's each will exponentially outperform the same budget spent on some Xeon's flung together. Equally you may well find that if the sort of number crunching you're after isn't able to work in parallel efficiently at all, you'll notice little or no difference to your hugely expensive setup to a single fast i7 box.
It's not just about preference, the approach you take really is key here, and without knowing *exact* examples of the tasks you're going to perform on these boxes you could well end up spending ten times as much on a system that performs 10 times as worse. No, really.
Source for below:https://en.bitcoin.it/wiki/Mining_hardware_comparison
To put an example out there, look at Bitcoin mining. I know you probably won't be using it for that, but still it's an example of huge amounts of number crunching that, because of its nature, performs exponentially faster on modern GPUs than CPUs. 3 HD 6990's will get a speed of over 2000 MHash/s (million hashes per second.) They'll set you back a tidy sum of approaching $2k, but give you 2 billion hashes a second out of it.
Now let's spend the equivalent sum in i5 2500k's, which set you back around say $150 each. Being generous, at the equivalent price you could get 13 i5s, which give you 20MHash/s each, generating a grand total of 260MHash/s, just over 1/4 of the performance of the above setup, using a crapload more electricity and generating a heck of a lot more heat.
But here's the thing, that's a task that can be optimised heavily towards GPGPU processing, and not all can. The tasks that can be optimised on GPUs, and the extent to which they can be modified depends on all sorts of things from the model of GPU you use (double floating point arithmetic is only supported in some for instance) and if your program can be parallelised and compiled to OpenCL source (sometimes this is difficult but do-able, sometimes impossible and CPUs are your only option.)
I'm not slamming the idea here, but you do need to do a lot more research of your own accord to ensure the project doesn't end up as an expensive inefficient doorstop, and the research is often a lot more involved and detailed than finding the best generic mainframe hardware out there. You need someone who's well versed in parallel computing and can go through the sort of thing you want to execute and work out if it can be sensible parallelised and if so if it can utilise OpenCL / CUDA effectively. It's not a job you can really do if you haven't got a fair bit of knowledge of those sorts of things already. I *could* do that in theory, though I'm afraid I've got way too much on at the moment to dedicate the time to it - but you may be able to find someone in your university who could help.
It could be a very good project, but you need to invest a lot more time in research. Unfortunately it's not just a case of providing a generic mainframe and having people drool at the mouth for it...