OK drekidd/tearinghairout2

This is a long shot, but the best I could come up with.

A bit of extended googling with 'dhcp reject xid' seems to suggest that the xid is something generated by the client (in this case pump) - that it presumably sends to the server in each request, and the server sends back in the response - so that it (the client) can keep track of which responses belong to which requests.
Apparently the client is supposed to generate the xid in such a way that no two values are ever used one after the other.

Now maybe (and this is complete guessing) your Knoppix dhcp client (pump) is basing the xid on the mac address (or part thereof) and since the same network card, with the same mac address is used in dual booting computer, it looks to your dhcp server that two different clients are trying to use the same xid, hence the reject message in your dmesg.

What if you try doing a complete reset of everything? Power down your dual boot computer, power down your nat/router/dhcp thingy, unplug the power cables from the wall, put them back in their original boxes, put the boxes outside your front door for a while, perhaps move houses, maybe think about emigrating. Then plug it all back in and boot Knoppix first (without booting XP).
Alternatively, try the DHCP request from another DHCP server today..

Please let us know how it goes - I love a challenge.
THO