I am really guessing as I have not enountered this issue before.
Try this as an admin user.
"Apple-Shift-u" will take you to the utilities folder. Find Terminal and open it.
" You will be asked for your password. Type it in and press return. You will get the unix prompt. Now type:
and press "return
". Hopefully the invisible volumes will mount. If they do you can do a "get info" and check the "ignore permissions for this volume" box on the invisible partitions.
You are logged into Terminal as God so it would be a good idea to quit Terminal before you do any damage.
Mount is the unix command to mount volumes and disks, sudo makes you supreme commander and allows you to bypass permissions issues. There is a modifier to force rebellious volumes to mount but I have no way to check it out at the moment.
Hopefully you won't need it.