No power & single rapid flashing light on battery indicator

You likely have a damaged charging logic on the main board. This often happens with knockoff chargers!

• Don't Replace Your MacBook Charger With a Cheap Knockoff
• Lacking safety features, cheap MacBook chargers create big sparks
• How to Spot A Fake Macbook Magsafe Charger

So you’ll want to invest on a REAL Apple unit if you get your system fixed: Apple - MagSafe chargers

So what to do? If you can find someone to fix your logic board would be one option. I’m not sure if thats the best option. The 2011 models had issues with the dedicated GPU’s failing (AMD GPU’s) as many people over stress the graphics the 2011 systems had. Surprisingly the 2012 logic boards (with a better Nvidia GPU) will work in your system. In fact I’m typing on such a system a late 2011 which now has a 2012 logic board. A very easy job with one minor mod needed on the LVDS cable as the 212 board connector is a hair narrower a few strokes with a nail file fixes that!

Here’s the needed part 15” Macbook Pro Logic Board 2.6 GHz i7, Apple P/N 661-6492

And here’s the guide to replace it MacBook Pro (15 Zoll, Anfang 2011, Unibody) Austausch des Logic Boards

And here’s what’s needed to get the display cable to work

I still prefer the original scissor keyboards, maybe next year I’ll look at getting a newer magic keyboarded system now that Apple has gone back from the failed butterfly.