I don't know what is wrong with the original remote. Possible the setup code for the receiver portion has been corrupted, but I have no idea how you would rectify that.
However, we do know that the VR309 (and other Kenwood receivers) use the NEC1 IR protocol device 184.0 for most functions, but uses 184.1 for the tuner functions. And of course the function numbers are also known.

For remotes made by Universal Electronics, it is possible to augment the built in setup codes with additional functions, and that may be a reasonable approach here. Presumably a Logitech Harmony would have Kenwood receivers in their database also. Controlling receivers with a universal remote is usually a little bit problematic because most universals have button labels and function assignments that are more geared to TVs and DVD players.

But you can program a UEI remote to control any function for the receiver.
Nearly any OneForAll, many Radio Shack, Comcast cable, Cox cable, Atlas remotes provided by other cable companies, and some high end Vizio remotes can use setup code Audio 1313, 1569, or 1570. Functions which aren't implemented can be added by entering a 5 digit EFC. If you don't have any of these remotes laying around, the RCA RCRP05B ($20 at Walgreens or Best Buy) is a good choice.