Hi.
What is the security type of the wireless network on TD-W8961ND? WEP or WPA?
The windows PCs are connected to the router by Ethernet cables? Or using wireless?
Have you tested the Android devices by connecting them to the wireless network of another router? If so, can they access Internet wirelessly?
Have you tried to adjust the wireless channel on the TD-W8961ND?

Security type: WPA2-PSK (i changed even to No Protection but didn't work better)
Windows PCs are connected with wireless adaptor type N
Yes, Android devices connected fine on other network
I tried different settings on router (B,G,N mode separately and all together, 20 MHz or 40 MHz) and now works better but not perfect
Now is on these settings:

Hi.
What are the model numbers of the Android devices?
If you change the security type to WPA-PSK/AES, can the Android devices connect to the network?
What error message can you see when the Android devices are connecting to the network?
BTW, wireless MAC filtering on the modem is disabled, right? You can double check at the bottom of the wireless page.

Hi

The Android devices have different versions: 4.1.2, 4.0.2, 4.0.1 and they behave the same

Changed security type to all in list even to NO Security but the problem persists

There is no error message, the devices connect to wireless network but the Wifi icon remains Gray (is Blue when working)
then need to turn Wifi Off/ON (from Android Settings) for 1 or 2 or 3 times (it depends can be 1 or 5 times) then it connect fine and Wifi icon turns Blue
sometimes it connects to internet even if Wifi icon is still Gray for a few minutes then turns Blue

Yes the MAC filtering is turned OFF

Insert DNS servers manually in DHCP settings

jimasek wrote

Insert DNS servers manually in DHCP settings

Tried that already, didn't notice any improvement

Did you make save and reboot router after those changes.

You can change the SSID(wireless network name) to a new one for a try. For the channel, you can change it to a static one, such as 6, 11 or the others, rather than Auto.

You can change the SSID(wireless network name) to a new one for a try. For the channel, you can change it to a static one, such as 6, 11 or the others, rather than Auto.