If it's not showing any items, then GetPortNames is returning an empty array.
If you look at the documentation, it says this:
Remarks
The order of port names returned from GetPortNames is not specified.
Use the GetPortNames method to query the current computer for a list of valid serial port names. For example, you can use this method to determine whether COM1 and COM2 are valid serial ports for the current computer.
The port names are obtained from the system registry (for example, HKEY_LOCAL_MACHINE\HARDWARE\DEVICEMAP\SERIALCOMM). If the registry contains stale or otherwise incorrect data then the GetPortNames method will return incorrect data.
So start by looking at the registry and see what it says the computer has.
Sorry, but we can't help you with this one - we have no access to your system!