Ben,
David brings up a very good point that I overlooked regarding your (new) Chinese clone Tech 2. Have you tested it on an applicable year GM vehicle other than your XLR? As long as it's getting 12 volts, the Tech 2 title screen with software rev should appear. Does it?
CC
You have received lots of good information. The following is much more time consuming and you need to be confident of what is going on if you want to try it, these notes are offered for you to use at your own risk. You need the full workshop manual to locate every module on each data bus.
Trying to diagnose a fault like yours at long range is tricky. The symptoms seem consistent with a fault on a data bus, it is not unknown for something to short it out, usually to ground but it could be to high. I haven't tried this on the XLR but I have tried it on other data buses, and that is to use a volt meter on the signal pin, with the other to ground. You need to be on the DC range and you should see something that isn't 0 volts nor is it 5v. The AC range should also give you a non zero result. If you have a scope you can look for the signal. This will give you a clue that there is at least a signal. You need a good quality meter with a high internal resistance.
If there is no signal, you need to unplug as much as you can easily get to (ALWAYS battery disconnected when plugging or unplugging). Ideally it would be everything, including the BCM. Once everything is unplugged take a voltage measurement to check that you haven't got a 12v signal (but you should know this from earlier). If you have 12v find the short to voltage. If you have a very low resistance to ground, you have a short to ground, which you need to find. If you haven't removed everything, this low resistance to ground check is not a reliable test. However, you should get to the point where there is no short to voltage or ground. If you don't pass, unplug more. If you do pass, plug one equipment at a time back in until the signal stops. The first module in is the BCM. If you unplug some modules and then get a working data bus, you have a clue where the fault lies.
You could work the other way round, unplugging one module at a time until you get a signal, but if you have multiple faulty modules it is harder to work out which are causing problems. Keep adding (good) modules, checking each step of the way that that signal is still on the data bus.
To be efficient, unplugging everything and then putting half back at a time is the least number of steps, however, given the time taken to plug and unplug modules it could be easier to work one at a time and hope it is one that is easier to get at which has the fault.
Take detailed notes. Once you have a suspect module, unplug and plug it to confirm that the fault appears and disappears, you need strong confirmation. Be aware that more than one module could be defective.