It's a good idea to reformat the machine, because who knows what all was run on it, and whether that may cause problems for you later or more so now. So it's a very good idea starting off from a clean slate - you will know what is installed, since you installed it.
In fact, I would never use a re-purposed machine without formatting it first. It's a security risk not formatting, and I would not want to chance my data etc on it. And since the machine was a server connected to the internet, there's even more reason to reformat it.
It will take you much less time to just start over than it would to go through potentially hundreds of thousands of files located on the system that could have been modified intentionally or maliciously.
A typical install of OS X usually takes less than 1 hour, usually around 35 minutes or so. Server may take longer, and all you really need to do is get it started which takes less than 5 minutes.
Additionally, you would not even need the original install disks, you can install any version of Mac OS X newer than what came with the server originally. Which might not be a bad idea since you are not really needing the features that a server version has to offer, based on what you said your were doing with the systems. But that really depends on what the Mathematica setup requires.
The main thing to tackle is booting up the xServes. Luckily, Intel xServes (which yours should be if they're running 10.6) have Lights-out-Management (LOM) that should support this sort of thing (all Macs support Wake-on-LAN, but that only works on a local network).
Apple Remote Desktop (ARD) has support for this. It looks like you'll need to forward a few ports (looks like 623 for the LOM, and then a bunch for ARD - do a search), unless you have some sort of VPN access to your home network.
The basic method will be, use ARD to power up your xServes, then remotely connect via ARD or a VNC client, build your Mathematica app and run it. Then shut down the xServes.
If you have a Mac with you, all this can be done via ARD, but if you want to do it with an iPad, you'll need your desktop Mac running whenever you want to remotely access it. The process there would be to enable Screen Sharing (in the Sharing panel of System Prefs), forward the appropriate ports, then use an app like Screens to connect to your desktop Mac, run ARD and Mathematica remotely on it, and do the above.
If you don't have your desktop Mac running all the time, you could in theory use Wake-on-LAN to turn it on, then access it with Screens, but that requires some other device to be always on, remotely accessible and capable of sending the WoL packet to the Mac (some routers are capable of this, typically with 3rd party firmware).
Best Answer
Yes - set up a DHCP reservation on your TimeCapsule using the Airport Utility of your choice. I prefer using a client ID so you can easily change things when you get a new server, but typing the MAC address in also works.