If it does not come to life at all on the split display the most likely problem is the battery compartment/wires or the on/off switch (Sensitivity).
Using any multimeter on continuity/ohms you can check that the switch is working. Connect the multimeter probes to the back of the Sensitivity switch of the detector and switch it On (the multimeter will should show a reading when switched on, and 0 when off - if the switch is good). Battery wise switch your multimeter to 9v DC and check where the two wires from the battery compartment connect to the internal electronics board with the multimeter probes, you should get a reading of 7 to 9v DC depending on battery life (the two 9V should be in parallel).
Regarding the detector it is a rebranded
Bounty Hunter Pioneer 202, as often done by Radio Shack.
Overview of the detector,
reviews, and
manual.
If the 10 minute two simple tests done with a multimeter do not show a fault in the battery compartment or switch itself, it will likely be more involved and perhaps a bad component on the board.