OK
Yhen I understand, still your connection problem is caused by the router as it work on the internal LAN. Check that your router has the latest software, lot of router are shipped with really bad firmware but normally they fix the bugs later. If it still do not work, try to borrow a Linksys or Netgear and test with, they always work.
The other boot up problem is not normal, and the hardware need to be checked, when and where is it bought, can you send the pcb to us ?
73 de mike