that isnt the modem log, pppd is a daemon, it activates itself when the modem makes a legit connection and is responsible for maintaining the connection and getting the IP address from the ISP.
you need to see what the modem log is, it could be a variety of places, /var/log/pppd or /var/log/modem/? or even in your home directory in a hidden file "."something, dont know where it is for sure
until you can get a look at exactly what the modem is doing there's no way to figure out whats happening
does netzero have any docs on this deal, last I recall they claim to be linux compatible