"According to our system, your Google Account or one of the Play Gift Cards you submitted isn't eligible for appeal."

 Similar to this post, but a different issue.

Problem:  You can't redeem a Google Play gift card, they need "more information", which you provide.

Then Google replies with "According to our system, your Google Account or one of the Play Gift Cards you submitted isn't eligible for appeal."  Meaning you've just lost your money.

Solution: It seems there isn't one.

The most likely explanation seems to be that gift card codes are being stolen between time of purchase and time of redemption.  Meaning by the time you try and redeem it, the funds are already gone.  But nobody seems to know for sure.

Although people love to hate on Google, it is not in Google's interest to deny legitimate customers use of their bought-and-paid-for gift cards.  Consistent failure to honor would destroy that part of Google's revenue stream.

The only solution, therefore, is to not buy Google Play gift cards.