The apn setting is taken from the settings I used with an earlier
Huawei modem (E392) that did work on this computer.

I have indeed tried the present modem on a windows machine to verify
that it worked at all. I just tested again, and managed to get a 4G
network connection using online.telia.se. I also removed the PIN, but
could not find any settings to restrict the connection to any
particular type of network on the windows network manager that Huawei
supplies.

Retesting earlier suggestions after that test on windows brings up somewhat different responses from the script and a steady blue light (not blinking) from the modem, but no working internet connection, and no wwan0 interfae visible as far as I can see:

$ ./huawei-4g-linux.pl
Huawei 4g modem (E3276 and possibly others) script by Janhouse (Janis Jansons).

Opening device: /dev/ttyUSB0
> ATZ
> OK
> ATZ
> OK
> ATQ0 V1 E1 S0=0
> OK
> AT^NDISDUP=1,1,"online.telia.se"
> OK
> ^NDISSTAT:1,,,"IPV4"
> AT^DHCP?
> ^DHCP: 31B54E4E,FCFFFFFF,32B54E4E,32B54E4E,12C743C3,13C743C3,150000000,150000000
> OK
warn, dhcpcd will not work correctly unless run as root
err, wwan0: open `/var/run/dhcpcd-wwan0.pid': Permission denied
Hexadecimal number > 0xffffffff non-portable at ./huawei-4g-linux.pl line 73.
' ignored at ./huawei-4g-linux.pl line 73.
Hexadecimal number > 0xffffffff non-portable at ./huawei-4g-linux.pl line 73.

You can close this script now or you can keep it open to monitor the link quality.

Link quality:
> AT+CSQ
> +CSQ: 19,99
> OK
> AT+COPS?
> +COPS: 0,0,"Telia",7
> OK
Link quality:
> AT+CSQ
> +CSQ: 18,99
> OK
> AT+COPS?
> +COPS: 0,0,"Telia",7
> OK
^C
Closing...
$$ ifconfig
eth0      Link encap:Ethernet  HWaddr 5c:9a:d8:ea:7a:17  
          UP BROADCAST MULTICAST  MTU:1500  Metric:1
          RX packets:0 errors:0 dropped:0 overruns:0 frame:0
          TX packets:0 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:0 (0.0 B)  TX bytes:0 (0.0 B)
          Interrupt:17 Memory:e2700000-e2720000 

lo        Link encap:Local Loopback  
          inet addr:127.0.0.1  Mask:255.0.0.0
          inet6 addr: ::1/128 Scope:Host
          UP LOOPBACK RUNNING  MTU:65536  Metric:1
          RX packets:48236 errors:0 dropped:0 overruns:0 frame:0
          TX packets:48236 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:0 
          RX bytes:12295946 (12.2 MB)  TX bytes:12295946 (12.2 MB)

wlan0     Link encap:Ethernet  HWaddr a0:88:b4:b7:3b:8c  
          inet addr:192.168.0.154  Bcast:192.168.0.255  Mask:255.255.255.0
          inet6 addr: fe80::a288:b4ff:feb7:3b8c/64 Scope:Link
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:526328 errors:0 dropped:0 overruns:0 frame:0
          TX packets:846132 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:115640447 (115.6 MB)  TX bytes:1189924701 (1.1 GB)

bmelinden@apis:~/bin/4g-connect-linux-master$ ip link
1: lo: <LOOPBACK,UP,LOWER_UP> mtu 65536 qdisc noqueue state UNKNOWN mode DEFAULT group default 
    link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00
2: eth0: <NO-CARRIER,BROADCAST,MULTICAST,UP> mtu 1500 qdisc pfifo_fast state DOWN mode DEFAULT group default qlen 1000
    link/ether 5c:9a:d8:ea:7a:17 brd ff:ff:ff:ff:ff:ff
3: wlan0: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc mq state UP mode DORMANT group default qlen 1000
    link/ether a0:88:b4:b7:3b:8c brd ff:ff:ff:ff:ff:ff

$ sudo ./huawei-4g-linux.pl
[sudo] password for bmelinden: 
Huawei 4g modem (E3276 and possibly others) script by Janhouse (Janis Jansons).

Opening device: /dev/ttyUSB0
> ATZ
> OK
> ATZ
> OK
> ATQ0 V1 E1 S0=0
> OK
> AT^NDISDUP=1,1,"online.telia.se"
> OK
> AT^DHCP?
> ^DHCP: 31B54E4E,FCFFFFFF,32B54E4E,32B54E4E,12C743C3,13C743C3,150000000,150000000
> OK
err, wwan0: ioctl SIOCGIFHWADDR: No such device
Hexadecimal number > 0xffffffff non-portable at ./huawei-4g-linux.pl line 73.
' ignored at ./huawei-4g-linux.pl line 73.
Hexadecimal number > 0xffffffff non-portable at ./huawei-4g-linux.pl line 73.

You can close this script now or you can keep it open to monitor the link quality.

Link quality:
> AT+CSQ
> +CSQ: 18,99
> OK
> AT+COPS?
> +COPS: 0,0,"Telia",7
> OK
^C
Closing...
$ ifconfig
eth0      Link encap:Ethernet  HWaddr 5c:9a:d8:ea:7a:17  
          UP BROADCAST MULTICAST  MTU:1500  Metric:1
          RX packets:0 errors:0 dropped:0 overruns:0 frame:0
          TX packets:0 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:0 (0.0 B)  TX bytes:0 (0.0 B)
          Interrupt:17 Memory:e2700000-e2720000 

lo        Link encap:Local Loopback  
          inet addr:127.0.0.1  Mask:255.0.0.0
          inet6 addr: ::1/128 Scope:Host
          UP LOOPBACK RUNNING  MTU:65536  Metric:1
          RX packets:48236 errors:0 dropped:0 overruns:0 frame:0
          TX packets:48236 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:0 
          RX bytes:12295946 (12.2 MB)  TX bytes:12295946 (12.2 MB)

wlan0     Link encap:Ethernet  HWaddr a0:88:b4:b7:3b:8c  
          inet addr:192.168.0.154  Bcast:192.168.0.255  Mask:255.255.255.0
          inet6 addr: fe80::a288:b4ff:feb7:3b8c/64 Scope:Link
          UP BROADCAST RUNNING MULTICAST  MTU:1500  Metric:1
          RX packets:526650 errors:0 dropped:0 overruns:0 frame:0
          TX packets:846421 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000 
          RX bytes:115679845 (115.6 MB)  TX bytes:1189951539 (1.1 GB)

$ ip link
1: lo: <LOOPBACK,UP,LOWER_UP> mtu 65536 qdisc noqueue state UNKNOWN mode DEFAULT group default 
    link/loopback 00:00:00:00:00:00 brd 00:00:00:00:00:00
2: eth0: <NO-CARRIER,BROADCAST,MULTICAST,UP> mtu 1500 qdisc pfifo_fast state DOWN mode DEFAULT group default qlen 1000
    link/ether 5c:9a:d8:ea:7a:17 brd ff:ff:ff:ff:ff:ff
3: wlan0: <BROADCAST,MULTICAST,UP,LOWER_UP> mtu 1500 qdisc mq state UP mode DORMANT group default qlen 1000
    link/ether a0:88:b4:b7:3b:8c brd ff:ff:ff:ff:ff:ff