If you're asking what you should do to fix the situation:
The first step should be to assume innocence (or in this case, ignorance) until proven guilty.
Unfortunately many developers don't understand licensing - or even realise that its a problem. In this case, I would first contact the author of the infringing software (it's not clear from your question which author you have already contacted - the infringing or the infringed?), and let them know that they are infringing the copyright of the GPL-licensed software.
Be careful to do this in a kind, 'just-letting-you-know' sort-of manner - don't accuse them of anything; just assume at first that they're not intentionally ignoring the license.
You might also want to suggest some appropriate paths to remedy. These might include:
- removing the GPL licensed code,
- replacing the GPL licensed code with an alternative permissive-licensed library if a suitable one exists, or
- relicensing the project under the GPL.
You might also point out - as EMBLEM mentioned in the comments - that the Code Project license is not free/open source.
If you get a favourable reply and changes are made, great - and well done for doing your part!
The next step to take really depends on what happens next.
If you don't get a reply after a suitable amount of time (say, a week or two), assuming the code is on a service such as GitHub, you could consider submitting a pull request to apply a different license. If you didn't get a reply to your question this is unlikely to be accepted, but for a busy developer who doesn't have time to consider a reply, a pull request of this nature might be just what is needed.
I wouldn't necessarily submit a pull request to remove the problematic code - unless of course you can also add a more permissive replacement. Just removing the problematic code will of course break the project, which is not really what a pull request should do (even if you are trying to make it compliant).
Finally: if your message has not been replied to; has been replied to negatively; your pull request with a more appropriate license has not been accepted; or the situation has otherwise not been resolved after you have tried your best, I would contact the authors of the infringed software. Document everything, and tell them each step you have taken.
In the end, the owner of the copyright on the infringed software is the only person who can take any further action if they choose to do so.
EDIT: Another option might be to advise gpl-violations.org of the alleged infringement. See their Violations FAQ for more information and an e-mail address to contact. They might not be able to do a lot on their own, but they might be able to help contact the author of the original software, and even help them with compliance action.
If you're asking what you should do if you want to use this software:
Unfortunately, you're not really going to be able to use this software as it sounds like it currently stands. I did originally suggest seeing if you could license your project under the GPL (which would be tough anyway given the need to also comply with the CPOL), but as ZeroUnderscoreOu and Zizouz212 pointed out in the comments, the software you want to use is rendered unlicensed by the fact that its own license violates another.
This means by making use of the software, which is effectively unlicensed, in your own project, you will yourself be infringing both the direct author's copyright, and the copyright of the original author of the GPL'ed portions.
Hopefully, you are able to get somewhere contacting either of the authors. Otherwise, I would start the search for an alternative package.