I cannot program the FPGA using signal tap when System Console is open. The other issue I am having is that Signal Tap analyzer won't trigger when I am accessing registers fro System Console (both tools are running).
Which board are you using and what is the type of download cable - USB Blaster II / USB blaster with JTAG header (9-pin). Does the board in question use micro-USB port or 9-pin JTAG connector for FPGA configuration? Generally, if the board uses JTAG headers, then you may have two headers, one for configuration and another for Signal-Tap and system console ( UART i/f ,etc).
The problem was that the tools were assigning the Sigal Tap instantiation to a different JTAG port. When I placed Signal tap and System Console on the same JTAG port, the problem was eliminated.