DVD Burning: Device Failed to Respond Properly

First thing to try is a PMU reset (assuming this is a G4 mini as listed in your profile), to ensure the device is correctly controlled.

To reset the PMU
-Unplug all cables from the computer, including the power cord.
-Wait 10 seconds.
-Plug in the power cord while simultaneously pressing and holding the power button on the back of the computer.
-Let go of the power button.
-Press the power button once more to start up your Mac mini.

If that doesn't help resolve this, and before you contemplate the cost of a new drive, it may be nothing more than a little dirt or debris. These slot loading drives seem a little prone to that. As such, a lens cleaner might be a good investment.

If it does turn out to be the drive is failing, I'd suggest you look at an alternative external drive rather than replacement internal. It's easier to do, externals are typically of better specification, and not being slot loading or in the air flow, not so prone to foreign matter.