I have no idea about how the HDMI works, but I had a dell laptop that would restart if a speaker with too low resistance was attatched to the output - 8 ohms would freeze the system, but if I connected another set of speakers (cheap computer speakers or headphones), the system would work. Are there any limits to the resistance of the speakers that can be used - if it is too powerfull, it may draw power away from the rest of the system, causing a restart (yet again, I have no idea about HDMI, and it has been a while since I had that system (I have not tried it with my t61 - no HDMI though)). Like Harryc said, it may also be a grounding loop, maby try grounding the adapter as well as the amp and computer?
If I am way off in anything, please let me know (this is my interpretation bases on my previous knowledge of sound equipment)
Elitebook 8440p, i5 520, 8gb, Samsung 840 SSD
Old/Not Working/Dead Laptops:
T61 7661CC2, 4gb, Windows 7 x64, 240gb intel SSD, 500gb Ultrabay drive
Toshiba Portege 7020ct
Thinkpad T41 23737FU
Dell Latitude LS