I have had similar problems with some notebooks (not just T4xx). I was using a 16 port KVM over IP switch from HP (with virtual media USB dongles), which was essentially a rebadged Avocent. Like you, the T410 I was testing would not output to the KVM. Pressing th FN+F7 (I think) to switch between display and external, would either do nothing, or cause the KVM attached monitor to go black, then into standby, go black, then into standby.
I initially thought it was something to do with EDID see this post:
Which unfortunately did not work. At the same time, we were experiencing problems with the KVM switch power supply, so I booked a call with HP, and they replaced with their G2 KVM switch. This was also an Avocent, but had a much better interface (full web based), and with this KVM, the notebook was able to work.
I did go back and test the old KVM before I sent it back, and found that if I used a 'normal' USB dongle, rather than one that had virtual media, then it would work. Same with a PS2 dongle. Not sure why, but the newer dongles didn't seem to like the switch, even though they would work with any desktop etc.