Strange dial-up Internet question

[Steven P. Ulrick]

Hello, Everyone :)
If this is off topic, I do apologize, but I assure you that I have tried
everything imagineable to figure out this problem, with no success so
far.  I figure with all the brilliant minds on this list, that someone
may have some wisdom for me :)

The problem is this: 
Sometimes when I attempt to connect to the Internet, the KPPP login
screen will give me a message about there being "NO DIAL TONE" (Kppp's
emphasis, not mine)  I'll go downstairs, get our cordless phone, and
guess what?  There most definitely IS a dial tone.  So, I go back
upstairs with the phone, which leads me to believe we have a dial tone,
and attempt to connect to the Internet.  Guess what?  "NO DIAL TONE"  I
figured out, apparently in a moment of inspiration, that if I attempt to
connect to the Internet with the phone turned on (the talk button pushed
to "on", just like I was going to call someone) that I can connect to
the Internet every time!  If I go through all that, turn the phone on
and connect to the Internet, and then shut the phone off, I still remain
connected to the Internet.  I must add at this point that even though it
will connect with the phone turned on, it connects at a pretty slow
speed (example: 26400 as opposed to our norman 45333+)  I have also
discovered that if I unplug the phone completely from the jack that it's
plugged into in the kitchen, that I cannot connect to the Internet.
One of the frustrating things about this is that the problem is
intermittent.  For example, I just had a guy from the phone company come
out and he replaced our network interface box on the side of the house
(it had been hit by lightning)  Well, I couldn't get this problem to
occur, for the purpose of showing it to him.  I also assumed that
because our interface box had been fried that that could have been the
cause of what I described above.  I just discovered that this is not the
case :(  I am sitting here typing this with our cordless phone on,
connected at a speed of only 26400, with a new network interface box on
the outside of our house, and a brand new U.S. Robotics 56k v92 Internal
PCI Fax/Voice modem in our computer, and the problem persists.
If anyone has ever run up against a problem like this, I would love to
have your wisdom on this.  If you feel this is off topic, I would prefer
that you would contact me off list, unless you feel your response could
help someone else.

To summarize, here are the things I've done to try to fix this:
1. New modem, as described above.
2. Had the phone company come out, and they replaced the network
interface box outside.

I will have my dad look at the inside wiring again, but I think that he
already did that.

In closing, I know that this might seem really weird, having to have a
phone turned on to be able to connect to the Internet, but I am NOT
making this up!

Anyway, thanks in advance for any wisdom you may be able to give me on
this :)
Steven P. Ulrick