Cannot Burn (HP ProBook 4510s CDDVDW TS-L633M)

Do you mean that you cannot burn the CDs altogether or it just produces errors during burning.
In either cases most of the time cleaning the lens with a CD ROM cleaner helps.
If it burns but gives errors then try another brand of CD-R. Use a slow burn speed when burning, it can be helpful. Try using another burning software.
Optical media and drives are getting increasingly cheap. If it fails often consider purchasing a new drive.

Yes no store bought brand is setup to be great quality. You will have to find either archive quality discs so that they have high compatibility and quality ratings or just by small amounts of brands till you find one that will work for you.
Cheers
Al