Fix a Boss GT-10 broken input jack - Roland Boss Gt-10 Guitar Effects Processor Gt10 Open

The first step would be to re-initialize the unit. Here's a link to the process-
BOSS Support Knowledge Base GT 10 Factory Reset Initialization

I would suggest cleaning the input jack, and if that doesn't fix it, replacing the jack.

XLR inputs often have a pad (attenuator) that is switchable for signal level.

The battery is connected via plugging in the input guitar cable ( a seperate contact is made at the jack). Sometimes this can be broken. Usually this failure is caused by someone stepping on or yanking a cable and the solder is broken at the jack/board attachment. This can be the input jack OR the power jack. Occasionally the circuit board or the traces on it are cracked, requiring jumpers to be installed on the board. In any case, open the pedal and look for these problems.

Open and look for broken solder at the jack... common occurence when people step on plugs or cables going into these. Also look for circuit board cracks around the connector and also around the power input connector.

Common problem is a broken solder connection where power jack is attached to the circuit board. SOmetimes the circuit board is cracked or solder broken. If board is cracked, jumpers need to be soldlered on to bridge the crack.

The half-way cord is the clue. Read up on unbalanced and balanced lines and TRS connectors.
One of these requires TRS connections and the signal is being carried on the RING of the TIP-RING-SLEEVE connector. Plugging in half-way the TIP touches the ring pickup contact. The emgs one MAY use TRS type cables and there may be a reason the signal and hot of these are reversed. If I could find schematics on all this equipment I could unravel the exact cause. You could make an adapter with a Stereo 1/4 inch plug and a 1/4 inch jack by wiring it to swap the tip and ring between them to use for connecting to the emgs guitar. ALSO verify you are using the SAME type guitar cable for both.OFTEN a TRS cable will NOT turn on the electronics when plugged into a guitar. Use an unbalanced instrument cable unless you have the XLR type output. Use of an adapter from the XLR type cable into the Boss will usually not work.

Make sure you are NOT using a TRS (stereo or three conductor cable) type cable. PLugging into the input should turn the pedal ON, not off. The switch on the jack may be broken or soldering to the circuit board may be broken OR worst case, there is a crack in the circuit board.

Plug your guitar into the input and a cord from one or both outputs to the inputs of whatever you are using. Meant to be run in stereo for best sound. Two guitar amps?

It's supposed to do that. An extra lug on the input jack is connected to the battery and/or power supply's ground.

So the only way to power off any pedal is to disconnect the input jack. If you use a power supply and power multiple pedals you can simply disconnect the power supply to cut power and avoid unplugging each one.