It's tough to see what that wood is where the screws go. Is it just plywood?
I would use an epoxy filler as a better product than the Durhams water putty. spasm3's glued in, over-sized dowel repair is an excellent solution also.
Depending on accessibility, a wood insert might work also:
http://www.theinsertcompany.com/index.php
That broken out hole on the left......if there is room, could you slide a T Nut shown below into the broken "slot" to work like a hollow wall anchor??