If you're having trouble opening a serial port, of if it doesn't show up in the HyperTerminal connection dialog, then it might be necessary to install the Windows serial port drivers.
Sometimes, an existing driver can become corrupted, necessitating a process of deleting and then re-installing the driver.
If you suspect that the Windows driver may be damaged (e.g., if the COM port does show up in the HyperTerminal connection dialog, but it doesn't work right), you need to delete the existing driver. First, open the Windows Control Panel, and then the System panel. In the System Properties window that appears, select the Device Manager:

Next, click on the Ports option, opening up the display of installed ports:

If the COM port you wish to use is not shown in the Ports list, then you probably just need to install it. Skip ahead to the next section, Installing the Device Driver.
To remove a suspected errant driver, select the driver you wish to delete (in the above screen, COM2 is selected), and then click Remove. You will be shown the following confirmation screen:

Click OK. Remember, you are just removing the device driver, not the device itself.
To install (or re-install after having deleted) the device driver, go back to the Windows Control Panel, and then choose Add New Hardware. You will be shown the "Add New Hardware Wizard" dialog:

Click Next to get going. Then you'll see the following screen:

It's best to allow Windows to go ahead and do this automatically, so just click Next. You'll have to click Next again to start the actual search-and-install process.
Windows will take a little while to do its thing, and if all goes well, the Add New Hardware Wizard will just finish without complain. Then, go back to the System Control Panel, choose the Device Manager tab, and look in the Ports area for new COM ports. If you didn't have a COM port entry for a port you think you have, it should now be installed; or, if you deliberately removed the driver, it should be back.
You can now return to the HyperTerminal test, to see if you can transmit characters to the Serial Interface/Charger Board and make the green SER LED blink.
It is possible that you will need to visit the CMOS settings for your machine. In some cases, CPUs may ship with existing serial ports disabled in the CMOS configuration. If this is the first time you're using a particular serial port, and Windows isn't finding it with the process described above, it may be a CMOS configuration problem.
Most PC's display a key sequence upon boot that should be pressed to enter the CMOS configuration.