I urge everyone having this problem to try to burn a disc using an external burner.
Also, if you have a Windows OS installed using BootCamp, try to burn a disc from a Windows boot.
You will find that in all cases you will not be able to burn.
This is due to a bug with the EFI firmware (the instruction set which controls devices on a hardware level at boot - grossly simplified). Replacing the logic board will fix this, because the replacement board will most likely not have a faultly EFI flashed to it. This corruption seems to happen when upgrading the EFI to a new version. For example, when first upgrading to Leopard (and SL) from Tiger, and now it seems also to Lion.
Conclusions:
Flashing firmware is a risky business in general. Apple should devise a sort of double redudancy method when flashing firmwares so that if something does go wrong, it is still possible to return to a previous, stable firmware (that is still existing on the chip). They had had this ability in the past, but removed it after EFI version 1.8 because Apple found that users were downgrading their EFI in order to us 3rd Party SSD, that Apple had not sanctioned, with higher bit transfer rates.
Recommendation:
Request/demand an EFI downgrade to 1.7 from an Apple Genius. The downgrade seems to re-flash the EFI without reading the previous tables (where the corruption would be). There is a Russian unofficial release from a Genius to downgrade 1.7 to 1.6. This fixed everyone's problems. Sadly once on 1.8 or higher, the downgrader no longer works (due to a version check).
I have given up on Apple on this issue. I have removed my SuperDrive and have replaced it with a second hard drive, and no longer burn discs. This is a problem when it comes to delivering media to clients, but in general, I hate DVDs since they are an obsolete storage medium and incredibly wasteful.