Hi Planas,
If Network controller is missing, it means that the Wireless drivers are not installed. Inspiron N5110 is usually shipped with the following types of cards:
Dell™ WLAN 1701 Half Mini-Card + BlueTooth 3.0
Dell™ WLAN 1702 Half Mini-Card + BlueTooth 3.0
Intel® Centrino Wireless-N1030 Half Mini-Card + BlueTooth 3.0
Intel® Centrino Advanced Wireless-N6230 Half Mini-Card + BlueTooth 3.0
Dell™ Wireless WLAN 1502 Half Mini-Card
Dell™ Wireless WLAN 1503 Half Mini-Card
Intel® Centrino Wireless-N1000 Half Mini-Card
Intel 6150 WiFi / WiMAX Half Mini-Card
You may check the Wireless card shipped with your system from the following link http://dell.to/13LWJoE -> type the Service tag of the computer -> click on System Configuration -> Original Configuration.
You can download Wireless drivers Here.
Hope this helps.