EA not taking trades
Print the important values with Comment on the chart and run the tester in visual mode - or use the debugger with hist. data.
"Print the important values with Comment on the chart" Sorry, I'm not really sure what this means. Are you saying show the proper entry/exit points on the picture I posted?
Or, edit the mql to add a comment at each price-related decision point?
"and run the tester in visual mode" yes, it's easy to see that entries and exits are missed.
"or use the debugger with hist. data" any chance you can give me some guidance on how to do this?
If you have access to the source code , put some print statements at the moment of the trade to make sure that you are getting there. Other issue could be lot size or account restrictions. A screenshot of the experts tab could be really helpful.
In the log file there is no indication that trade was even attempted.
These are valid entries according to the rules. Trades are at least executed in tester.

My EA isn't taking trades on demo. I works in Strategy Tester.
I've checked the three more obvious culprits, live trading, auto trading, allow automated trading.
I've tried three different accounts on three different brokers.
It should look like this pic from tester. The closes you see there are not entirely accurate. I'm working on that.
Any suggestions?