problems with new computers modem

I just got a new dimension E510, the first day I tried to connect up to the internet, and was receiving a message, NO dial tone, after hours of trying to figure out was was wrong I shut the computer off.  The next morning I turned on the computer and everything was fine, I was able to hook up to the internet, figured problem was solved.  Wrong.  3rd day, I turned computer on, went to hook up to the internet, and now as given a message, my phone line was busy.  first I didnt change anything on my computer from the day before when it was working right and was connected.  2nd my phone line was not busy, I unplugged everything in my house hooked up to the phone line, I plugged 3 different phones into the wall jack, every one worked fine.  I hooked up my older dell computer to the same wall jack, it worked fine, ( I was online with it, talking to a dell rep).  So there is nothing wrong with my phone line, my phone cords, or my wall jack.  The rep had me run the modem helper, it gave me a code 70, no dial tone at modem, I told the rep, he had me download a driver which I did and installed, well that didnt fix it, and I lost the rep online.  so as a last resort, I ran a phone cord from my old computer to my new E510 (hooking the computers up together), then ran another phone cord from my old computer to the wall jack, and was able to sign on to the internet with the E510, thru my old computer.  What could be wrong?  Is my modem in the new computer shot?  After using it one time?  Any help or suggestion will be very much appreciated, I have emailed dell, but so far the rep was no help at all.