Wireless internet causes connection to drop

I have a Netgear WGR614 v5 wireless router connecting several
computers to a DSL modem. My problem is that the internet started
dropping out frequently. Every 5 minutes or so, the bubble would pop
up saying "Network cable unplugged", then it would reconnect within
seconds and I could continue surfing.
I disabled the wireless connection on the router. It never drops.
But as soon as I enable wireless on the router, the connection starts
dropping again.

I tried changing frequencies to just about every one available.
I moved the router to the top shelf away from any computers etc.
I got rid of my cordless phones (for other reasons)
I upgraded the firmware on the router to the latest version.
I have disconnected computers and had the same result no matter which
computer is connected.

Still my connection drops whenever I have the wireless enabled on the
router. The lights on my modem tell me the internet connection is
still present, but the connection to the router is what is dropping.

Any suggestions would be greatly appreciated.