Compuer shows no sign of tablet connection (SGH-T779 Samsung Galaxy Tab 2 10.1 for T-Mobile)
This might sound crazy, and I do not recommend anyone try it, but...

I had tried cleaning the female charging port on the tablet with alcohol and q-tips and had no luck.  I decided to use the tip of a mechanical pencil (metal tip) to scrape the contacts to see if they had build up.  I put the metal tip in to scuff them up and (since the tablet was on), a huge spark shot out of the tablet and it immediately shut off.  I assumed I fried it, but it turned back on... ...and worked perfectly from that point on.  It was then recognized by my computer.  

Obviously, this is somewhat crazy and I don't recommend people try this.  I had tried every method of connection from the far ends of the internet with no luck.  Somehow it worked normally after this point.  Could the spark/firework show have cleaned the contacts?  I know that some pins are for charging (which it would do fine) and other pins are for data.

My tablet is now working.