i seriously would regret getting any consoles after v.7. my v.9 has also been giving me issues. common problems with a v.9 is the laser lifespan and that annoying LA-6508 chip frying too. chipping it too requires another hardware mod to protect the laser. anyways...
1. (broken piece) ok, that broken cylindrical piece could of been soldered back on if the pad from where it was broken from had solder on it. oh well!
you'll prob need a new motherboard and you can get one for $24 at www.ps2parts.com if you want to swap the old one with the new one.
2. (no power) the power supply could of already had it's toll. you can buy a new one at the same site mentioned above for a replacement.
3. (controllers not vibrating) i really don't know anything on this but if you replaced the controller port hub with one from a different version then that could be your problem unless that replacement hub was already faulty too.
ps2parts.com has this good deal that anything on the console can be fixed and replaced (no matter what) for $50 with free shipping on domestic order! get this while it's hot.
PS1/SCPH-7501 | MM3 modchip
PS2 v9 | 250GB hdd | PS3 component cable | katana 32mb mc
PS3/CECH-2001B | 250GB hdd | 3.65 ofw