This happened when I issued the NETSTAT command:
TCP informix:turbo as2000:1260 CLOSE_WAIT
TCP informix:turbo as2000:1261 CLOSE_WAIT
TCP informix:turbo as2000:1262 CLOSE_WAIT
TCP informix:turbo as2000:1263 CLOSE_WAIT
Is this why we can't get more connections? (I have NT4 Server, Informix 7.31 TC2, fewer than 100 users.)
You're on 7.31 TC2. What Service Pack is your NT 4.0 on? I believe 7.31 works with SP5 or later, but I'm not sure.
I'm not exactly sure how to do this, but could you try killing some of the TCP connections manually? Maybe by starting/stopping the network rather than doing a complete reboot. If you can regain connectivity after killing some of the TCP/IP sessions, then it's pretty obviously a problem linked to the number of sessions. Otherwise, is there anything you have been able to do to restore connectivity other than stopping/starting the database?
E-mail me a copy of your ONCONFIG file and I'll take a look at it.