Q: MacBookPro service issues at Apple store

I bought a MacBook prod 15" a few years back. It's a late 2011 model. I am having problems with the battery as it's crossed the recharge cycles and due for a replacement.

I booked an appointment with a local Apple store and went there to get it replaced. When I got served (almost 45 minutes late from my scheduled appointment), the guy told me that he couldn't find the purchase date of my Mac and if I can provide him the date. Now, it has been good 5+ years since I bought it and I couldn't remember the date. He said they can't do much unless I provide them the date.. nice...!!! that really helps. Upon asking why is it so important as the Mac is more than 4 years old and It's out of warranty. (Also, I knew that, I need to pay for the new battery). He said, from where ever you bought your Mac, the shopkeeper needs to register it online at the time of the sale and he seems to not have done that. Now, is this my problem? also, the electronics retailer whom I bought it from has gone in receivership just a couple of months back so, I can't even go back to that store to get the purchase date.Just spoke to Apple support and the support person also couldn't find my details on their system. I even tried https://checkcoverage.apple.com/updateDop to find the details and it asks me for the purchase date.

since past few weeks, I am also having issues with the display where I can see pink vertical lines on my screen every now and then. Upon searching Mac support forums it appears to be caused by the display card. I found this link https://www.apple.com/au/support/macbookpro-videoissues/ which indicates a knows issue with Apple Macs around early 2011 and they qualifies for a free service to address the issue. Now without a purchase date, not sure how do I get these fixed?

This is beyond frustrating, you buy an expensive product due to it's market reputation for quality and end up with almost no support. For the price you pay for MacBooks, you could easily buy a far better laptop and not to worry about any of these issues. Does anyone know how do I raise this with Apple's top management? At the moment I feel like going in circles. Any help would be much appreciated.