Robert,
Based on your internet link, it appears you are in Tasmania so for you to call Davis directly in the United States may be a bit expensive. Thus, I would suggest that you contact whoever you purchased your VP2 from and find out what kind of technical support they offer for a new weather station. Of course, if you discover the problem was caused by having the #4 DIP switch in the on position, then this is a moot point but something to think about how and where to contact support for any future problems you may encounter with your Davis VP2.
You mention the low battery message was present before you changed the battery. Has it been on since you initially installed your VP2? And, as has been suggested, is it possible that the battery was installed backwards?
And lastly, to determine whether there are any other VP2 units in your area and what channel they are operating on, simply turn off your ISS and then let the console sequence through looking for any signals it may find. If there are any in your neighborhood, this will tell you what channel they are on. Then, simply disable any channel that is active and set your ISS to the "lowest" channel number that is not in use. That will optimize your data times for your area. All of this can be found in the Vantage Pro2 Console Manual. Go to Chapter 4 - Troubleshooting and Maintenance and go to the "Check Console Reception" section. It also refers to Screen 1: Active Transmitters on page 10 where you can see the active transmitters in your area. Going on to Screen 2: Configuring Transmitter IDs - Wireless Only, will allow you to manually turn on or off various channels. I would highly recommend that you disable (turn off) any channel that you are not using for your ISS. This will eliminate interference from any future VP2's that get installed in your area. Of course if one pops up on your channel you will need to consider moving to another channel to avoid interference between the two stations. From personal experience, I had a new VP2 installation pop-up a block away from me and I started having intermittent errors. The ONLY way I found the problem was to turn-off my own ISS and then let the console go through its search for nearby ISS's. Once I found the culprit, I changed channels and my intermittent problems disappeared.
Sorry, I know this is long-winded but being new, I can imagine how overwhelmed you can get when things don't work as they are supposed to.