Full Wi-fi/ethernet signal but no internet
Here is a step-by-step guide for you:


Temporarily disable any Firewall/Internet Security solution/packet filter on your Mac (like LittleSnitch/Hands Off!/Kaspersky Internet Security etc.)
Connect to the administrative interface of your router with a working Mac.
Make a note of the internal interface (probably 192.168.0.1 in your case)
If your router uses MAC-filters to control access, check that the Mac in question isn't blacklisted or is whitelisted if you use whitelists. To get the MAC-address of a Wi-fi interface, open System Preferences -> Network -> Choose "Wi-fi" -> Advanced -> Hardware -> MAC Address on the Mac without internet access.
On the Mac without internet access disable all interfaces in the network preferences pane except the Wi-fi interface by choosing the interface and clicking on the little gear -> "Make Service Inactive". You might have to unlock the lock in the left bottom corner first.
Choose the Wi-fi interface and click 'Advanced'
Choose the TCP/IP settings, choose to configure IPv4 manually and enter the proper IP-address, netmask and gateway address (enter the IP-address found in step 2 as gateway address). In your example  this should be any address not already in use in the range of 192.168.0.2-192.168.0.254 as IP-address, 255.255.255.0 as netmask and 192.168.0.1 as gareway.
Choose the DNS tab next to the TCP-IP settings.
Enter 8.8.8.8 as DNS server. This DNS server is a public one from Google.
Save/apply the settings
Open Terminal.app
Flush any existing routes by entering route -n flush several times.
Flush DNS cache with dscacheutil -flushcache;sudo killall -HUP mDNSResponder. You have to enter your admin password to complete the task. This works with Mac OS X 10.9 (Mavericks) only. If another OS X is installed use the appropriate command.
Now ping the gateway address and the DNS server with ping -c 5 192.168.0.1 and ping -c 5 8.8.8.8. The command sends 5 pings to the specified address. To stop pinging - if you didn't include the -c  option - just enter ctrlC.
If you get a successful answer, quit Terminal. If you didn't get an answer, enter ifconfig en1 and re-check the proper settings of your Wi-fi interface. en1 should be your Wi-fi interface.
Return to the network preferences and reenable all other interfaces. Check that the Wi-fi interface is on top of the list. To reorder the list click on the little gear -> "Set Service Order..." and rearrange the interfaces.
Now open a browser of your choice and try to connect to an arbitrary site.
If you have internet access now, you may replace the Google DNS server with DNS-servers of your ISP or simply add them.




This guide didn't solve the problem.

After some very deep investigations (kudos also to John Keates) we found out that a misconfigured dnscrypt/dnscrypt-proxy was the culprit.