Cisco router with BRI dial-in refuses to negotiate PPP calls

[ATC]

Cisco 2600 series router running "c2600-is56i-mz.120-5.T" with a 8-port BRI module, PPP dial-in fails to negotiate properly.

This problem may or may not apply to other models and IOS revisions.

[ATC]

Turn on ppp debugging using the following commands:
"debug ppp authentication"
"debug ppp negotiation"

Now try connecting. If messages like these loop a few times, you're out of luck:
"00:04:03: BR1/0:2 LCP: O CONFREQ [REQsent] id 8 len 24
00:04:03: BR1/0:2 LCP:    MagicNumber 0x501284DB (0x0506501284DB)
00:04:03: BR1/0:2 LCP:    MRRU 1524 (0x110405F4)
00:04:03: BR1/0:2 LCP:    EndpointDisc 1 Local (0x130A01696E7374616C6C)"
It's supposed to work but it doesn't. We don't know why, and gave up after wasting 4-5 days on the problem. Use a different IOS image.

We recommend you try "c2600-is56i-mz.113-10.T" if you don't need AAA, or "c2600-is56i.120-5.T" if you don't need encrypted tunnels.