It will be hard to find a MOBO + CPU that will utilize your DDR3 memory, that's way he suggested a new platform.
It's a bit out of your budget indeed, but it will provide a much better support for newer games and drivers, so IMHO is worth spending a bit more on it.
Current parts that would utilize your owned pieces aren't much cheaper as well but are considerably worse...
Best bet is try to get the Ryzen 3 and a cheap B350 MOBO or a Intel G4560 and BIOS updated H110 MOBO