Let me set the scene. I currently have a 1.1Ghz box with 512MB RAM and a small but sufficient 40GB hard-disk drive. This drive is partitioned into two partitions, the first one is about 25GB in size and contains a Windows XP install - this needs to be left intact. However the second partition, all 14GB of it, is what I can play with.

Re-partitioning this partition isn't the problem - I just don't know what to install. I currently have the CD's for both Mandrake 10 and Fedora Core 2 sitting in front of me, but...

I am aware of a problem that existed with Fedora Core 2 and Mandrake 10 where it wasn't advisable to install either on the same HDD as a Windows installation. Something to do with messing up the boot-sectors.. I don't know the details of this bug, all I know is that it exists.

Has there been any sort of patch for this problem, or is there anything I can do to stop anything from happening if I were to go an install either of the two distro's?

Any kind of information regarding this subject will be appreciated. Thanks for your time.
- Matt.

To my knowledge, Mandrake doesn't have any issues dual booting with WinXP.
Fedora Core 2, however, has. You should cast your eyes over this article: http://lwn.net/Articles/86835/ and do a search here at LQ for dual booting FC2 & XP before you take the plunge and install FC2.
I ran Mandrake 10.0 alongside XP without any problems - the default Mandrake bootloader (lilo) even detects Win partitions automatically and adds them to the boot list so you don't have to configure it when the install is done.
Both Mandrake and FC2 are good, solid distros, but I can only recommend Mandrake as I actually use it - so much so that I don't have Windows on my box anymore.