You don't need to manually pull the axes on startup. This is more for gantry tools than BT series tools.
In some cases, if the switch proves to be good (from your test with screwdriver they sound like they are ok) - the controller card can burn out the I/O portion of the controller card - and cause the problems you are running into. Not saying 100% that is the case, but be aware...it happens.
For now, set the limits to OFF. You can leave the wiring intact if you want or just pull the wires out of the block. To use the tool, just drive it around using SK mode, then position the tool where you want 0,0 to be. Then Z2 (or ZX and ZY by themselves). To Zero the Z, you can use the plate if you verify that Input 1 is working. You only need the input 1 wire and ground. On some tools, you need to put the clip to the spindle (just clip it on anything metal near the Z...one of the nuts holding the Y V-rollers is good enough) and then touch the plate to the bit. See if input 1 lights up on the DRO each time you touch it. If so, you can run the C2 command - which will call up C:\SBParts\Zzero.sbp - hold the plate until it touches twice...don't pull it away after the first touch.
If the Zzero plate is not working, you can manually set the Z. SK (keypad mode) also has a 'Fixed' mode where you can check it, enter a small value, like .01", and incrementally 'dink' whatever axis that distance each key press. It makes it easier to sneak up on where you need to be ever since SB screwed up the software when the Desktop machines came out...Anywho...Just get the bit where you want it and ZZ. Now Z zero is set. Once the axes are zeroed, there is NO NEED to zero them again until you turn off the control box or lose power, OR change to another tool (Z).
Anyway - Before you unplug anything or do the Zzero test, be sure to run TS (tools setup) and follow the prompts for the Homing routine and Zzero plate. Be SURE to first, park the tool at physical 0,0 AND be sure to follow the prompts all the way to the end and click on 'I'm Done' - or the settings will not be updated. This could be some of the issue you are having with the limits - so try TS first. If not, try the other things I mentioned.
Yes - of course it's best to have limits on the machine...but in reality - aside from conveniently locating 0,0 when you enter the C3 command - you don't really need them...nothing is going to fly apart, the motors will time/alarm out if they meet resistance etc...so it's not a deal breaker if you want to play around and do some cutting right now today.