I have 3 Linkstar modems whose ethernet ports appear bad. When a cross-cable is connected from any of them to a PC,  it shows that the network cable is unplugged.

I tried to open the modem to see the possibility of resetting it, and observed it had a RJ11 port with "console" written underneath it. Apparently, I will need that cosole cable to Hyperterminal into it to try to reset it. But I dont know the pin configuration for making RJ11 to DB9 console cable.

Please can anyone help me to fix these problems?

I bet you damaged the rj45 port while your teleport was writing its sw/fw at bank one. So even if you used a console cable and try connect there via hyperterminal, you'll not succeed. In fact i guess it's xilinx microcontroller that stops functioning due to bad image in the eeprom. In fact it's a technical issue that viasat should publish, since downloading SW in the linkstar can occur at each HWreset, and having missing file downloaded (while setting the command lmesetprisw 1 or lmesetprifw 1) can prohibit you telnetting the terminal in order to manually repair it!! I encontered such problem, and viasat refused to help solving it!!!

Check that your cross over cable is not faulty in some way.  Are any of the insulating spacers bent sideways over the gold contacts ?  

Are you using correct gateway, subnet and IP address?. I think you should still get a green light on PC ethernet socket however.

Failure to communicate via the ethernet was a known fault on some early linkstars. Return to supplier for RMA.

In desperation you could try this https://www.satsig.net/linkstar-serial-cable.htm but warranty will no longer apply and read about the conditions and risks first ...

When commissioning a linkstar do not power off or interfere with it at all while the hub is interacting with it.  I prefer to leave the BUC cable disconnected until the receive aspect if fully aligned and ready.  This may save a premature and unexpected commissioning starting, which you might easily interrupt if you have not finished dish alignment.

Best regards, Eric.