I have fresh installation of Slackware 14. It came with NetworkManager by default but cannot connect to mobile broadband network via ZTE USB modem.

My device is
Bus 003 Device 009: ID 19d2:0031 ZTE WCDMA Technologies MSM MF110/MF627/MF636

EDIT:
I forgot to tell you that KPPP can do internet connection via that modem (actually, I'm using it now).

Having this problem with this device too:

Oct 13 12:47:29 elitebook NetworkManager[1050]: <info> Activation (ttyUSB2) starting connection 'Mobile Network via ZTE connection 1'
Oct 13 12:47:29 elitebook NetworkManager[1050]: <info> (ttyUSB2): device state change: disconnected -> prepare (reason 'none') [30 40 0]
Oct 13 12:47:29 elitebook NetworkManager[1050]: <info> Activation (ttyUSB2) Stage 1 of 5 (Device Prepare) scheduled...
Oct 13 12:47:29 elitebook NetworkManager[1050]: <info> Activation (ttyUSB2) Stage 1 of 5 (Device Prepare) started...
Oct 13 12:47:29 elitebook NetworkManager[1050]: <info> Activation (ttyUSB2) Stage 1 of 5 (Device Prepare) complete.
Oct 13 12:47:29 elitebook NetworkManager[1050]: <warn> GSM connection failed: (32) Sending command failed: device is not enabled
Oct 13 12:47:29 elitebook NetworkManager[1050]: <info> (ttyUSB2): device state change: prepare -> failed (reason 'unknown') [40 120 1]
Oct 13 12:47:29 elitebook NetworkManager[1050]: <warn> Activation (ttyUSB2) failed.
Oct 13 12:47:29 elitebook NetworkManager[1050]: <info> (ttyUSB2): device state change: failed -> disconnected (reason 'none') [120 30 0]
Oct 13 12:47:29 elitebook NetworkManager[1050]: <info> (ttyUSB2): deactivating device (reason 'none') [0]
Oct 13 12:47:29 elitebook NetworkManager[1050]: nm_system_iface_flush_routes: assertion `ifindex > 0' failed
Oct 13 12:47:29 elitebook NetworkManager[1050]: nm_system_iface_flush_addresses: assertion `ifindex > 0' failed
Oct 13 12:47:29 elitebook modem-manager[2650]: <info> Modem /org/freedesktop/ModemManager/Modems/3: state changed (connected -> disconnecting)
Oct 13 12:47:29 elitebook modem-manager[2650]: <info> Modem /org/freedesktop/ModemManager/Modems/3: state changed (disconnecting -> connected)
Oct 13 12:47:29 elitebook NetworkManager[1050]: <info> disconnect failed: (32) The serial port is not open.

I am able to connect via Nokia E52 smartphone connected via USB/microUSB cable and I see substantial difference in logs - there is /dev/ttyACM0 instead of /dev/ttyUSB2. I will investigate it further.

The device mode is detected correctly so as I see it, there is no need for usb_modeswitch:

ostry@elitebook:~$ lsusb
Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub
Bus 002 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub
Bus 003 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
Bus 004 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
Bus 005 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
Bus 006 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
Bus 007 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
Bus 008 Device 001: ID 1d6b:0001 Linux Foundation 1.1 root hub
Bus 001 Device 004: ID 04f2:b053 Chicony Electronics Co., Ltd
Bus 003 Device 002: ID 03f0:171d Hewlett-Packard Bluetooth 2.0 Interface [Broadcom BCM2045]
Bus 004 Device 002: ID 08ff:2810 AuthenTec, Inc. AES2810
Bus 006 Device 002: ID 192f:0416 Avago Technologies, Pte.
Bus 002 Device 014: ID 19d2:0031 ZTE WCDMA Technologies MSM MF110/MF627/MF636
Bus 002 Device 008: ID 0421:01d0 Nokia Mobile Phones

I also preventatively removed SD memory card from the device during the tests in hope, that it will lower the probability that its functionality as USB memory key will collide with its functionality as mobile broadband modem. Now Nautilus does not open it automatically (nothing to open).