HELP!!! "Charging is not supported with this accessory" suddenly happening CONSTANTLY with iphone 4

Question

Suddenly without warning my IPhone 4 has been giving me a "charging is not supported with this accessory error" every time I plug it into ANY charging device.  That means my car charger, USB to the PC... USB to a macbook pro... Directly to the wall with the included charger, etc.  It doesn't matter.  I guess I'm past the 1 year warranty so Apple is not any help.  Essentially I'm supposed to accept that my $200 (with a contract) phone has a 1 year life span and that I should be completely fine with it becoming useless out of nowhere.  Here's some facts.
#1 - It has nothing to do with 3rd party accessories.  One day it was working... one day it wasn't. 
#2 - I cleaned lint out of the charging port on the phone.  That was the first thing I tried. I used compressed air to blow it out, I used a soft bristle tooth brush...  It's lint free.  It has nothing to do with lint.  I understand this is the most likely cause of the problem.
#3 - When I plug it into a PC or macbook via USB, I'm able to access the IPhone 4 like I ALWAYS have.  In other words, I can see pictures, I can back up the phone, I can restore the phone, I can transfer music, sync, etc.  So this would presumably rule out the idea that it's the dock connector, right?  Why would USB work, but the charging function will NOT work?
#4 - On that note, I was able to update the software to the latest version 5.1.1.  That was one of the first things I tried.  No dice.  I still get the "charging not supported with this accessory" error literally every time I plug it in with a yellow triangle icon... Seen here for example: http://tapatalk.com/mu/4c5f44af-af20-d86c.jpg .
#5 - So since it's not charging, the phone inevitably dies.  Here's the weird part... if I leave it plugged into the wall/pc/mac/car when it's dead... eventually it will charge enough to turn back on.  But once it's back on... that **** error will pop back up, it will stop charging... and inevitably die again.  So then... that would suggest that it actually IS capable of taking a charge... it's just that something in the software is preventing it from charging when the software is active, no?  Am I off base here?
#6 - So I decided I'd take it to the genius bar to have them look at it.  Right before I did that, I got the brilliant idea to try using an alcohol swab on the dock connector just to make sure it was super duper extra clean.  Oddly enough, it suddenly started working without the error.  It was working on every charger I tried.  Wow.  I thought I had fixed it.  A day later it started happening again, though.  Bizarre.  I've tried the alcohol swab thing again and it didn't make a difference... maybe it was just a fluke.... the one day I take it to the Apple genius bar and it works.  Go figure, right? 
#7 - The only helpful thing the tech at the Apple Genius Bar was able to tell me was that the phone did NOT have any kind of water damage.  That rules that out.  No water damage in the charging dock OR the headphone jack.  So there's that.
#8 - Since it's no longer under warranty... I took it upon myself to buy a replacement battery via Amazon.com and installed it myself.  Didn't make a difference... still the same error.  
What, if anything, can I try?  Could it really be the dock connector?  Should I try replacing the dock connector?  Is there any software-related thing I can try?  Has this happened to anyone else?   Apple has essentially told me it's my problem.  From my perspective... any product that randomly stops working a little over a year is a faulty product.  I'm not pleased at all.

Answer 1

Tried at least 6 different cables.  It isn't the cable.  All of them worked one day... then stopped working the next day.  My girlfriend has an identical Iphone 4 and all of the cables still work for her. 
Interesting point on the data and power using different pins.  So your suggestion would be to replace the dock connector?  Found this on Amazon: http://www.amazon.com/Apple-iPhone-dock-connector-cable/dp/B003UGVOO2/ref=sr_1_1 ?ie=UTF8&qid=1338277549&sr=8-1 ... and found a tutorial online:  http://www.ifixit.com/Guide/Installing-iPhone-4-Dock-Connector/3147/1#.T8SG_sXWu -o  ... Sounds like that might be my best bet here.
It's just odd to me that the phone gives me that error and refuses to charge... then inevitably dies.  But once the phone is dead, it starts charging enough to actually turn back on.  Isn't that slightly odd?