New DC's and modchips

[clueless]

I have pretty much ascertained that the DC I have (which I picked up a few weeks ago - manufactured Dec 2000) will not play CDR's. I have burned about 20 coasters trying every method possible - I cannot even get the boot disk working with Nero or Clone...
The question I have, is whether the modchip which is available is likely to fix this or not.

Thanks in advance