I have a LG U8120 phone
I have not been using it so far with my computer - ie phone manager to manage messages, contacts, diary and more importantly to listen to MP3s.

I have installed the software - Opened up software called
LG Phone manager - There is a connect icon
when I press on this - dialog box window appears with

Connecting ... please wait

After a few second I get the message

Phonemanager (title of dialog box)
Failed to connect to the mobile handset, Please check the COM port and connect in idle screen.

What do I have to do to connect to my phone so I can download a few MP3 tracks and manage my "contacts list"

The reference to the com port in your error message indicates that there is a problem with the connection cable. You never mentioned any cables though. You're not trying to do this through wireless are you? That won't work unless you have bluetooth or something.

My phone came with a USB connection cable - one end connects to my phone and other end USB (end) connects to the laptop.

I have installed the drivers.
When I connect my phone with this cable and looked under "device manager" under modems if I look under this icon:
LGE U8XXX USB WMC Data Modem
LGE U8XXX USB WMC Modem


Under Ports(COM & LPT) icon:
LGE U8XXX USB WMC Device Manager (COM8)
LGE U8XXX USB WMC Modem OBEX Interface (COM7)

I have infa red on the phone and laptop but again don't know how to operate this either