Why can't my iMac see contents of discs or burn DVDs?

Question

Contents of DVDs don't appear and I cannot burn DVDs.
About two months ago I became unable to burn a DVD.
One month ago I became unable to see the contents of DVDs, though my iMac can recognize and read an audio CD..
I've tried accessing information from commercial as well as Sony DVD-R 16X discs made by a friend using his iMac—to see if my friend's discs were blank, we opened them in his iMac and found all the programs; I tried again on my iMac and still can't see any content.
I have repaired permissions using Disc Utility, but the problems were not solved.
Discs appear on the desktop as "Untitled DVD".  When I open "Disc Utility", the discs themselves do not show up, and the image for "SuperDrive" seems greyed out; still, when I select "SuperDrive" I can get "Info" and instructions for erasing a disk.
I was advised to open System Preferences>Users & Groups, unlock the lock, click on the little plus icon, make a new administrative account, then log out & into the new account; but the problems were not solved.

Answer 1

Hi Babowa,
I inserted my friend's DVD (proven to have content), saw the iMac could see no content, then went to: Apple > about this Mac > more info > System Report > Disc Burning and got the report below which says the disc is blank:
OPTIARC DVD RW AD-5680H:
  Firmware Revision:          3AHB
  Interconnect:          ATAPI
  Burn Support:          Yes (Apple Shipping Drive)
  Cache:          2048 KB
  Reads DVD:          Yes
  CD-Write:          -R, -RW
  DVD-Write:          -R, -R DL, -RW, +R, +R DL, +RW
  Write Strategies:          CD-TAO, CD-SAO, CD-Raw, DVD-DAO
  Media:
  Type:          DVD-R
  ID:          SONY16D1
  Blank:          Yes
  Erasable:          No
  Overwritable:          Yes
  Appendable:          Yes
  Write Speeds:          2x, 4x, 6x, 8x
Twice I inserted a commercial DVD and it was automatically ejected both times.