wireless completely disappeared

Question

I have a new dell E5580 running xenial 16.04. I cloned my old drive (on an E5570) and everything works perfectly except for wireless. When I type nmcli dev I get this output

DEVICE     TYPE      STATE      CONNECTION 
enp0s31f6  ethernet  connected  ARE wired  
lo         loopback  unmanaged  --       

i.e,. there's no indication of any wireless device. Similarly lspci | grep -i wireless returns nothing.

I can use wireless when I boot ubuntu from a pen-drive, and when I am in windows (I have a dual boot setup) so it's obviously a software problem.

When I click on the network icon in the tray there's no mention of WiFi at all.

At the suggestion of @David_Foerster, I'm cutting and pasting output from the commands he suggested. The first is from my old machine, for which wireless works.

lspci output
02:00.0 Network controller [0280]: Intel Corporation Wireless 8260 [8086:24f3] (rev 3a)
        Subsystem: Intel Corporation Wireless 8260 [8086:0050]
        Kernel driver in use: iwlwifi
        Kernel modules: iwlwifi

lshw output
  *-network               
       description: Wireless interface
       product: Wireless 8260
       vendor: Intel Corporation
       physical id: 0
       bus info: pci@0000:02:00.0
       logical name: wlan0
       version: 3a
       serial: a4:34:d9:9a:31:61
       width: 64 bits
       clock: 33MHz
       capabilities: pm msi pciexpress bus_master cap_list ethernet physical wireless
       configuration: broadcast=yes driver=iwlwifi driverversion=4.4.0-104-generic firmware=16.242414.0 ip=192.168.1.206 latency=0 link=yes multicast=yes wireless=IEEE 802.11abgn
       resources: irq:132 memory:ef100000-ef101fff
  *-network
       description: Ethernet interface
       product: Ethernet Connection (2) I219-LM
       vendor: Intel Corporation
       physical id: 1f.6
       bus info: pci@0000:00:1f.6
       logical name: enp0s31f6
       version: 31
       serial: d4:81:d7:5b:ae:b9
       capacity: 1Gbit/s
       width: 32 bits
       clock: 33MHz
       capabilities: pm msi bus_master cap_list ethernet physical tp 10bt 10bt-fd 100bt 100bt-fd 1000bt-fd autonegotiation
       configuration: autonegotiation=on broadcast=yes driver=e1000e driverversion=3.2.6-k firmware=0.8-3 latency=0 link=no multicast=yes port=twisted pair
       resources: irq:133 memory:ef300000-ef31ffff

lisusb output
Bus 002 Device 007: ID 13fe:5500 Kingston Technology Company Inc. 
Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub
Bus 001 Device 018: ID 046d:c00c Logitech, Inc. Optical Wheel Mouse
Bus 001 Device 019: ID 413c:2010 Dell Computer Corp. Keyboard
Bus 001 Device 016: ID 413c:1003 Dell Computer Corp. Keyboard Hub
Bus 001 Device 015: ID 046d:c00c Logitech, Inc. Optical Wheel Mouse
Bus 001 Device 013: ID 413c:2513 Dell Computer Corp. internal USB Hub of E-Port Replicator
Bus 001 Device 011: ID 8087:0a2b Intel Corp. 
Bus 001 Device 017: ID 04a9:1792 Canon, Inc. 
Bus 001 Device 014: ID 413c:2513 Dell Computer Corp. internal USB Hub of E-Port Replicator
Bus 001 Device 004: ID 1bcf:2b91 Sunplus Innovation Technology Inc. 
Bus 001 Device 003: ID 0a5c:5800 Broadcom Corp. BCM5880 Secure Applications Processor
Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub

The second is cut and pasted output frin the new machine, for which wireless doesn't.

lspci output
02:00.0 Network controller [0280]: Intel Corporation Device [8086:24fd] (rev 78)
        Subsystem: Intel Corporation Device [8086:0050]
03:00.0 3D controller [0302]: NVIDIA Corporation Device [10de:134e] (rev a2)
        Subsystem: Dell Device [1028:07a8]

lshw output
  *-network UNCLAIMED     
       description: Network controller
       product: Intel Corporation
       vendor: Intel Corporation
       physical id: 0
       bus info: pci@0000:02:00.0
       version: 78
       width: 64 bits
       clock: 33MHz
       capabilities: pm msi pciexpress cap_list
       configuration: latency=0
       resources: memory:ef100000-ef101fff
  *-network
       description: Ethernet interface
       product: Ethernet Connection (4) I219-LM
       vendor: Intel Corporation
       physical id: 1f.6
       bus info: pci@0000:00:1f.6
       logical name: enp0s31f6
       version: 21
       serial: a4:4c:c8:4d:e9:73
       size: 1Gbit/s
       capacity: 1Gbit/s
       width: 32 bits
       clock: 33MHz
       capabilities: pm msi bus_master cap_list ethernet physical tp 10bt 10bt-fd 100bt 100bt-fd 1000bt-fd autonegotiation
       configuration: autonegotiation=on broadcast=yes driver=e1000e driverversion=3.2.6-k duplex=full firmware=0.1-4 ip=192.168.1.220 latency=0 link=yes multicast=yes port=twisted pair speed=1Gbit/s
       resources: irq:131 memory:ef300000-ef31ffff

lsusb output
Bus 002 Device 001: ID 1d6b:0003 Linux Foundation 3.0 root hub
Bus 001 Device 004: ID 8087:0a2b Intel Corp. 
Bus 001 Device 003: ID 0c45:6717 Microdia 
Bus 001 Device 005: ID 0a5c:5834 Broadcom Corp. 
Bus 001 Device 001: ID 1d6b:0002 Linux Foundation 2.0 root hub

The outputs are different in several respects and hopefully suggest where the problem might be. The lspci command returns two wireless related lines for the old machine, which are absent on the new machine. The lshw command on the new machine returns a first line which says UNCLAIMED. On the old machine, this command returns description as Wireless interface

Thanks very much for all your help and patience! Leo