Most likely there's an open in the battery connection to the mainboard. Do you have access to a PX2 (9V AC 2000mA) power supply? The power supply input is a separate pathway than the battery.

If you live close to a Guitar Center, you might consider bringing your DL4 in and testing it with one of their PX2's (there should be a few in the showroom floor).

If battery power is the only way you want to power-up the DL4, then you'll need a service repair tech open up your unit and diagnose the point of failure and fix it: http://line6.com/support/serviceCenters/