pppd died unexpectedly. Where to look?

[Hans]

System: Acer Travelmate 512T running Slink. Generic PCMCIA modem.
Goal: setting up ppp connections to two different ISPs.
Done: configured pppconfig, kppp, resolv.conf (for DNS)
The problem: pon/poff dials in, but refused to connect. kppp the same, and the log from pppd is as follows for both ISPs):

Nov 28 19:07:19 mack pppd[407]: pppd 2.3.5 started by root, uid 0
Nov 28 19:07:19 mack pppd[407]: Using interface ppp0
Nov 28 19:07:19 mack pppd[407]: Connect: ppp0 <--> /dev/ttyS1
Nov 28 19:07:20 mack pppd[407]: peer refused to authenticate
Nov 28 19:07:26 mack pppd[407]: Connection terminated.
Nov 28 19:07:27 mack pppd[407]: Exit.

Did I mis-configure something or are the ISPs at fault here? Please some pointers so I can continue digging, thanks you. -- Hans