DNS problems

[#1]

I need some help here.
Tonight my wife's work laptop will not connect to the internet via my home wifi. It is seeing and connecting to the wifi, but having DNS problems which means it can't connect to the internet. It used to work, and while I haven't changed anything at home her work have recently done a load of changes.
All my devices are working.
I need some little baby steps to sort this out. Anyone?
P.S. This is not AFAIK anything to do with Plusnet.

[#2]

Open a command prompt by clicking Start, typing 'cmd' (minus quotes) in the Search field (or after clicking Run if using XP) then press enter.
Type 'ipconfig /all' (minus quotes) and press enter. What happens? Are you able to paste the results here?
Using the same command window, can you traceroute to an IP address using 'tracert 212.159.6.10' (minus quotes)?

[#3]

Can't easily cut-and-paste...
So retyping...
Tracing route to 212.159.6.10 over a maximum of 30 hops
1 1ms 1ms 1ms 192.168.0.254 (my router)
2 * * * Request timed out.
3 * * * Request timed out.
4 * * * Request timed out.
5 18ms 22ms 24ms 212.159.6.10
Trace complete.
Will try to copy the ipconfig stuff via a USB stick...

[#4]

Quote from: AxeMurderer

Can't easily cut-and-paste...

Right-click the command window, left-click 'Mark', highlight the text you want to copy as usual, right-click it once (should copy it to your clipboard), then come here and paste it as you normally would.

[#5]

It's not that! The problem is on a machine that isn't currently connecting to the internet so I can't paste it here directly...

[#6]

Although if you were reminding me that I could cut and paste to a shared drive, good point. So...

>ipconfig /all
Windows IP Configuration
  Host Name . . . . . . . . . . . . : VIM000587a
  Primary Dns Suffix  . . . . . . . : lan.venture.co.uk
  Node Type . . . . . . . . . . . . : Hybrid
  IP Routing Enabled. . . . . . . . : No
  WINS Proxy Enabled. . . . . . . . : No
  DNS Suffix Search List. . . . . . : lan.venture.co.uk
                                      home.gateway
Wireless LAN adapter Wireless Network Connection 2:
  Media State . . . . . . . . . . . : Media disconnected
  Connection-specific DNS Suffix  . :
  Description . . . . . . . . . . . : Microsoft Virtual WiFi Miniport Adapter
  Physical Address. . . . . . . . . : 00-26-82-B5-8A-75
  DHCP Enabled. . . . . . . . . . . : Yes
  Autoconfiguration Enabled . . . . : Yes
Wireless LAN adapter Wireless Network Connection:
  Connection-specific DNS Suffix  . : home.gateway
  Description . . . . . . . . . . . : Broadcom 4313 802.11b/g/n
  Physical Address. . . . . . . . . : 00-26-82-B5-8A-75
  DHCP Enabled. . . . . . . . . . . : Yes
  Autoconfiguration Enabled . . . . : Yes
  Link-local IPv6 Address . . . . . : fe80::c4e6:392f:349e:743%14(Preferred)
  IPv4 Address. . . . . . . . . . . : 192.168.0.6(Preferred)
  Subnet Mask . . . . . . . . . . . : 255.255.255.0
  Lease Obtained. . . . . . . . . . : 14 December 2011 19:27:44
  Lease Expires . . . . . . . . . . : 15 December 2011 21:41:12
  Default Gateway . . . . . . . . . : 192.168.0.254
  DHCP Server . . . . . . . . . . . : 192.168.0.254
  DHCPv6 IAID . . . . . . . . . . . : 369108610
  DHCPv6 Client DUID. . . . . . . . : 00-01-00-01-13-FB-17-57-1C-C1-DE-9D-EB-82
  DNS Servers . . . . . . . . . . . : 2001:470:20::2
                                      192.168.1.20
  NetBIOS over Tcpip. . . . . . . . : Enabled
Ethernet adapter Local Area Connection:
  Media State . . . . . . . . . . . : Media disconnected
  Connection-specific DNS Suffix  . : lan.venture.co.uk
  Description . . . . . . . . . . . : Intel(R) 82577LC Gigabit Network Connecti
on
  Physical Address. . . . . . . . . : 1C-C1-DE-9D-EB-82
  DHCP Enabled. . . . . . . . . . . : Yes
  Autoconfiguration Enabled . . . . : Yes
Tunnel adapter isatap.{CD70993C-36D7-48DF-AF4F-DE8EAC4B56BB}:
  Media State . . . . . . . . . . . : Media disconnected
  Connection-specific DNS Suffix  . :
  Description . . . . . . . . . . . : Microsoft ISATAP Adapter
  Physical Address. . . . . . . . . : 00-00-00-00-00-00-00-E0
  DHCP Enabled. . . . . . . . . . . : No
  Autoconfiguration Enabled . . . . : Yes
Tunnel adapter isatap.home.gateway:
  Media State . . . . . . . . . . . : Media disconnected
  Connection-specific DNS Suffix  . : home.gateway
  Description . . . . . . . . . . . : Microsoft ISATAP Adapter #2
  Physical Address. . . . . . . . . : 00-00-00-00-00-00-00-E0
  DHCP Enabled. . . . . . . . . . . : No
  Autoconfiguration Enabled . . . . : Yes
Tunnel adapter Teredo Tunneling Pseudo-Interface:
  Media State . . . . . . . . . . . : Media disconnected
  Connection-specific DNS Suffix  . :
  Description . . . . . . . . . . . : Teredo Tunneling Pseudo-Interface
  Physical Address. . . . . . . . . : 00-00-00-00-00-00-00-E0
  DHCP Enabled. . . . . . . . . . . : No
  Autoconfiguration Enabled . . . . : Yes
Tunnel adapter isatap.lan.venture.co.uk:
  Media State . . . . . . . . . . . : Media disconnected
  Connection-specific DNS Suffix  . :
  Description . . . . . . . . . . . : Microsoft ISATAP Adapter #3
  Physical Address. . . . . . . . . : 00-00-00-00-00-00-00-E0
  DHCP Enabled. . . . . . . . . . . : No
  Autoconfiguration Enabled . . . . : Yes

[#7]

Don't suppose her work have been making their network IPv6 compatible have they?

   DNS Servers . . . . . . . . . . . : 2001:470:20::2
                                       192.168.1.20

Seems odd that your primary server is an IPv6 address. You could try going to the wireless adapter properties via the Network applet of the control panel and make sure the properties for the IPv6 protocol stack are set to obtain an IP address/DNS servers automatically (if they're not already?)

[#8]

Her work were supposed to be 'just' moving to Office 365. But their IT people do some odd things...
Her laptop is already set to obtain an IPv6 address automatically. But IPv6 could be something to do with it... I was/am an IPv6 triallist; I'm not using the IPv6 account at the moment, but I have left my router IPv6 enabled. This has been harmless to all my other devices but it is worth a try at disabling it.

[#9]

No, no difference. 

[#10]

Quote from: AxeMurderer

Her laptop is already set to obtain an IPv6 address automatically. But IPv6 could be something to do with it... I was/am an IPv6 triallist; I'm not using the IPv6 account at the moment, but I have left my router IPv6 enabled.

Ah, that would explain it then, probs a red herring in which case. Come to think of it though the IPv4 address is odd, I'd expect it to be the router address (192.168.0.254) or one of our's/a third party's DNS server addresses.
Does it make any difference if you go into the IPv4 properties and explicitly set the DNS to the following?

212.159.6.10
8.8.8.8

Do you have the same problems if the laptop's wired rather than relying on the wireless connection?