FPGA + SRAM – floating inputs of SRAM during configuration of FPGA

You've got the wrong device.

In order to program the SPI Flash using the indirect JTAG method, you need to right click on the FPGA and select Add BPI/SPI Flash. It'll ask for the device type and your programming files. The type should be SPI Flash M25P16 according to this document, page 106. Then highlight the SPI Flash you just added and select the Program operation. When the Programming Properties comes up, Xilinx recommends you tick the Verify and Erase before programming options.

These instructions, and more, are available in the Spartan-3A FPGA Starter Kit Board User Guide, the programming instructions for the indirect method start on page 103.

Note:

If the above doesn't work, check your Jumper settings. Taken from the User Guide. Page 103.

When reading an SRAM bit, both column wires can be driven high (precharged) before raising the row wire high; one of them will then be pulled low, while the other one won't and will remain in the precharged state.

To write an SRAM bit, one of the column wires should be pulled low while the other is either precharged or pulled high. Turning on the access transistor won't do much on the side whose column is pulled high, but the access transistor on the other side will overpower the high-side PFET within the memory cell; doing that will in turn turn on the high-side PFET on the other side.