Now I don't know if this is correct or not, a faulty HDD could also be to blame I think, and Xbox Scene forums may be a better place to ask about this problem. The only drawback is that the forums can be quite elitest and some of the regulars on there can appear very abrupt when replying to posts. I think that is because the vast majority of them are yanks and so have the American "I know best so put up or shut up" attitude.
Anyway, if you have your Xbox hard-modded, ie with a chip, then it is best to know what type of chip is in the box, ie Xenium, Xecuter 2 or 3 etc. That way you can check the documentation for the chip for troubleshooting and problem solving.
I have an Xecuter 3 (X3) chip and it sometimes does what you are saying, except this happens after streaming a video in XBMC fails and the box locks up, requiring a cold reboot. I have the little Xecuter led on the front of my box and instead of lighting up blue for a normal boot, it turns on red, then the box reboots a couple of times and finally the eject button led flashes orange and green. Removing the power cable from the box for a minute or so allows the box to boot normally.
However, the Xecuter adapter that fits onto the Xbox motherboard has a tensioned gold wire that goes to a tiny hole on the motherboard, and if this pops out, it can also cause problems similar to what you have described.
What I would suggest is that you, or someone familiar with the Xbox, open the case and have a look at the chip to see what type it is (it will be on the top of the chip - all the manufacturers love to brag about their product) and then take it from there. And the chip manufacturers always refer to themselves as team something-or-other, ie team xecuter, team xenium etc, so google the name of your chip and head to the chip homepage.
I hope some of this helps. It's a pity you're on the other side of the Irish Sea from me. I'd love to have a look at this in person.