Have a HP mini 1030NR that had full Karmic with virtually no problems. Have placed clean install of Lucid Lynx on this machine and it works while plugged in. Opened a document in Open Office and took off power to print at a printer in the next room. The mouse and unit froze totally. No difference with power management removed or reloaded.
So long as plugged on power, can manipulate the document, etc. I can try bringing the printer to the mini and expect even this to work. The sound, webcam, keyboard, mouse, and other functions generally work fine. Broadcom 43xx loaded poorly with this loading and showing its light lit and even worked for a while. While the unit is on, the Broadcom chip is not detecting wireless, but that is the only other problem encountered.
I could try netbook remix or moblin, but prefer the full interface and it all worked till now, even with the small innards of this machien.
Not seeking answer to Broadcom, though I may try to fiddle with this, having resolved it in the past with driver 'tweaks'