my 2011 macbook pro won't church or turn on connected to mains??

Reset SMC. http://support.apple.com/kb/HT3964

Choose the method for:

"Resetting SMC on portables with a battery you should not remove on your own".

If this does not help, contact Apple.

http://support.apple.com/kb/TS1365

Best.

I went through the same issue with my 17" 2009 macbook pro. No luck. I even went to the extraordinary effort to crack open the case and remove battery and power up to make sure it was not a battery issue. [Well, you disconnect the cable, no need to physically remove the battery]

(Note, I verified this was safe because I found the official apple support manual and this was listed as one of the diagnostic steps to determine if the battery died). -- don't do this unless you know proper anti-static procedures and have the right tools for the job.

But point of this response is I do have good news. I took it to the apple store today, and the genius bar tech told me about a flat rate repair for $310.00. He said as long as I didn't damage anything like spilling a coke on it, then this flat rate price covers replacing logic board, battery, even both if need be. Heck, buying a replacement logic board, which is worst case scenario costs more than twice this amount.

P.S. there are also two hardware SMC reset pins (labeled SMC reset) on the motherboard, but I did not manually short them to force a hardware reset even though I saw a web hit explaining I should do this. Reason is that this was not mentioned in the apple service manual, and since I was going to the apple store anyway in hopes it was just a battery then I wasn't going to risk doing something that wasn't documented in the official support manual. So personally, I wouldn't try that unless you don't have the $310 for a sure thing repair.

Bottom line, I'm tickeled to death that Apple has a $310 all-inclusive deal. The 800 number for apple tech support person said the motherboard will cost around $800 and he wasn't aware of any special "deals".