Using JTAG to "explore" a board without damaging it?
Quick Answer:  You can't do it.

Long Answer:  Yyyyyoooouuuu ccccaaaannnn''''ttt dddddooooo iiiittttt.

But seriously, without having a schematic you won't be able to drive the JTAG interface without running some risk of damaging things.  JTAG lets you essentially set "most" of the pins on a chip into some sort of GPIO pins, and then lets you read or write their state.  If you don't know what they are connected to then you run the risk of setting a pin to an output while some other pin is also driving it.  That would create some "bus contention" which could damage the parts.