Here's the output I thought might be helpful...let me know what else you need to get this fixed.
dinh@dinh-VGN-Z590N ~ $ iwconfig
eth0 no wireless extensions.
lo no wireless extensions.
wlan0 IEEE 802.11abgn ESSID:off/any
Mode:Managed Access Point: Not-Associated Tx-Power=15 dBm
Retry long limit:7 RTS thr:off Fragment thr:off
Power Management:on
dinh@dinh-VGN-Z590N ~ $ rfkill list all
0: hci0: Bluetooth
Soft blocked: no
Hard blocked: no
1: sony-wifi: Wireless LAN
Soft blocked: no
Hard blocked: no
2: sony-bluetooth: Bluetooth
Soft blocked: no
Hard blocked: no
3: sony-wwan: Wireless WAN
Soft blocked: no
Hard blocked: no
4: phy0: Wireless LAN
Soft blocked: no
Hard blocked: no
dinh@dinh-VGN-Z590N ~ $ ifconfig
eth0 Link encap:Ethernet HWaddr 00:1a:80:d7:78:45
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:18 Memory:ee900000-ee920000
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:16436 Metric:1
RX packets:4 errors:0 dropped:0 overruns:0 frame:0
TX packets:4 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:0
RX bytes:240 (240.0 B) TX bytes:240 (240.0 B)
wlan0 Link encap:Ethernet HWaddr 00:21:5d:70:31:84
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)
dinh@dinh-VGN-Z590N ~ $ rfkill unblock all
dinh@dinh-VGN-Z590N ~ $ sudo /usr/lib/linuxmint/mintWifi/mintWifi.py
[sudo] password for dinh:
-------------------------
* I. scanning WIFI PCI devices...
-- Intel Corporation WiFi Link 5100
==> PCI ID = 8086:4232
-------------------------
* II. querying ndiswrapper...
-------------------------
* III. querying iwconfig...
eth0 no wireless extensions.
lo no wireless extensions.
wlan0 IEEE 802.11abgn ESSID:off/any
Mode:Managed Access Point: Not-Associated Tx-Power=15 dBm
Retry long limit:7 RTS thr:off Fragment thr:off
Encryption key:off
Power Management:on
-------------------------
* IV. querying ifconfig...
eth0 Link encap:Ethernet HWaddr 00:1a:80:d7:78:45
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:18 Memory:ee900000-ee920000
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:16436 Metric:1
RX packets:4 errors:0 dropped:0 overruns:0 frame:0
TX packets:4 errors:0 dropped:0 overruns:0 carrier:0
collisions:0 txqueuelen:0
RX bytes:240 (240.0 B) TX bytes:240 (240.0 B)
wlan0 Link encap:Ethernet HWaddr 00:21:5d:70:31:84
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)
-------------------------
* V. querying DHCP...
-------------------------
* VI. querying nslookup google.com...
;; connection timed out; no servers could be reached