|A PC or laptop not seeing the tablet seems to be a common problem but I didn't find anyone complaining their laptop died afterwards. Maybe it was becasue you didn't go through the 'safely remove' process but then usually that only applies if they're connected and transferring data. Besides, without it showing you couldn't go through the removal process anyway.|
Make sure the laptop battery is charged or charging. I suppose it could be problem with the USB port or power adapter jack as you suspect but if you were careful making those connections they should be OK.
If you do get it running this google search may help in connecting the tablet:
The first few hits were helpful. The exact fix may depend on your tablet model number.