Three things ocur to me:
1. In one post you said that, with an external booster battery hooked up, the lights and dash come up but the starter still will not turn over the engine! Is that true? That would say there is a lousy connection somewhere, OR the booster battery itself is just about as bad as the one in the car! Or, less likely but still possible: the car battery is so bad it actually is shorting out inside and killing power even from the external booster. Test for this by disconnecting the car's battery and using ONLY the external one for a try.
2. I have seen a remote starter "cause" a dead battery in an odd way. You push the button and the car tries to start, but fails. So it tries again, fails again. And again .....
Eventually after all these tries the battery is drained and it is STILL trying! Of course, you're in the house and don't even know this is happening. All you know is, you get to the car and it is not running and won't turn over. The original problem here is hard-to-start engine, not battery.
3. Since you're in Western Canada, try this. In our city, Canadian Tire shops will charge and test a battery for you FREE if you bring it into the parts counter. A few times I have taken in the dead battery, asked them to charge for 6-10 hours, then gone back to have it tested (it cannot be tested when dead - must be charged first, anyway). In each case I was lucky and the battery was OK. I took it home, re-installed and no more trouble. Talk about the price is right!