Might it be worth your while posting some pictures of the box so that someone can tell us which - if any - other brand names were available on the same device, as it's fairly unusual for there to be no alternative versions of the budget brands.
Failing that, how about trying to trace it through with a view to using a generic part from Maplin or your local equivalent supplier of components - very few of which are unique to one maker or model.
I hadn't heard of GPX until now and have spent a most enjoyable few minutes searching just in case the one you're after fixing was out there in cyberspace. I didn't find that, but I did like their take on the portable component style of box, in the shape of a very clean silver one currently on eBay, whose design has elements of JVC and Sansui to it.
Good luck with your search for information and welcome to this forum.