Testing IO's with boundary scan would be easy,at least with a boundary scan tester.I work with tools from JTAG Technologies,and it would be a matter of 5minutes to make a test like that,but it runs on their hardware.
But normally ,when you are in doubt about the integrity of a chip,it would be soldered on a board,wouldn't it? So you will need to know everything about this board (schematics,netlist,datasheet of all chips etc...).and then you can make a board test around your FPGA.You tell the tools which pins to drive high or low,which pins to sense 0 or 1 in order not to make any short circuits.
and about the internals of the FPGA .... you just can't test it,that's true.I have a CycloneII chip here with defect internal RAM,all the rest is OK (or at least the parts that I use in that particular design)