I cannot get the rig to talk to the computer
The most likely problem areas are
1) the COM port speed setting for the rig is not the same as the computer's COM port speed. See here for a table of valid COM port speeds for each rig.
2) the COM port number is not correct. See here for changing the COM port number.
3) (FT-857/D, FT-897/D using rear CAT socket) the function of the CAT/Linear/Tuner socket is not set to CAT. Use menu item 020 to change the setting to CAT.
4) (FT-857/D, FT-897/D using rear CAT socket) the function of the Mic socket is set to CAT. Use menu item 059 to change the setting to NOR or RMT.
5) there is a cabling problem between the rig and computer. See here for cable types for each rig. For RS232 attached rigs be sure you have pins 2 and 3 connected the right way round. The VR-5000 and FT-847 need them 'crossed', the FT-450, FT-920 and FT-1000MP Mark V need them 'straight'.
6) your cable includes a circuit to convert between RS232 and TTL voltage levels AND it draws power from the serial port. In this instance you must tick either/both the commands Raise DTR and Raise RTS on the Options menu. This is not required for the Yaesu CT-62 cable which is powered from the radio.
7) if you can get the rig to change frequency, but you cannot get back any status information and the timeout counter keeps increasing then you probably have a break in the receive data line into the PC, or have connected the receive line to pin 4 (of a 9-pin plug).
8) there is a fault in FTBCAT. Please contact the author if the program has problems communicating with the rig.
9) An unlikely problem is that the rig requires a CPU reset to sort out some oddity that has lodged itself in its memory.