I had exactly the same thing and solved in the same way.
Our JTAG was not working anymore while the board worked for more than a month. TDI was measuring 50 Ohm to ground.
We suspected an FPGA problem and no board problem.
I disconnected the normal powersupply and I applied 5V to TDI from seperate power supply and ground to the ground of the board. This to "burn" the short in the FPGA... small change that it worked but as I could not use JTAG anyway it was no big loss if the FPGA would burn completely.
The resistance was increasing. After applying the voltage for a second it was 70 Ohms, applying again for 5 seconds it became 150 Ohms but still not working. After another 10 seconds it became 2 Ohms and I put the board aside because I thought the board was now completely defective.
However, after reading this thread I tried it again. TDI became 5k and I can program the JIC into the board.
FPGA was a Stratix III 3SL70F780C4N.
How can this happen? Is it a bad FPGA... or could short on TDI caused by electrostatic discharge?