Thanks for your replies. We did try resetting the router, but it didn't work.
Here are the results from "ipconfig /all".
This is what I got on the computer with faulty connection, when the computer was connected to the wifi.
I hope I'm posting the relevant part...
Wireless LAN adapter Wireless Network Connection:
Connection-specific DNS Suffix . : Home
Description . . . . . . . . . . . : Atheros AR1111 WB-EG Wireless Network Adapter
Physical Address. . . . . . . . . : 94-DB-C9-5B-42-77
DHCP Enabled. . . . . . . . . . . : Yes
Autoconfiguration Enabled . . . . : Yes
IPv6 Address. . . . . . . . . . . : fd00::75de:3b4a:fde3:625d(Preferred)
Temporary IPv6 Address. . . . . . : fd00::a511:f430:d5cc:e68f(Preferred)
Link-local IPv6 Address . . . . . : fe80::75de:3b4a:fde3:625d%14(Preferred)
IPv4 Address. . . . . . . . . . . : 192.168.0.49(Preferred)
Subnet Mask . . . . . . . . . . . : 255.255.255.0
Lease Obtained. . . . . . . . . . : Saturday, May 11, 2013 11:09:25 AM
Lease Expires . . . . . . . . . . : Sunday, May 12, 2013 11:09:35 AM
Default Gateway . . . . . . . . . : 192.168.0.1
DHCP Server . . . . . . . . . . . : 192.168.0.1
DNS Servers . . . . . . . . . . . : 192.168.0.1
205.171.2.65
NetBIOS over Tcpip. . . . . . . . : Enabled
Here's what I got from the same computer, but when the wifi was dropped:
Wireless LAN adapter Wireless Network Connection:
Connection-specific DNS Suffix . : Home
Description . . . . . . . . . . . : Atheros AR1111 WB-EG Wireless Network Adapter
Physical Address. . . . . . . . . : 94-DB-C9-5B-42-77
DHCP Enabled. . . . . . . . . . . : Yes
Autoconfiguration Enabled . . . . : Yes
IPv6 Address. . . . . . . . . . . : fd00::75de:3b4a:fde3:625d(Preferred)
Temporary IPv6 Address. . . . . . : fd00::a511:f430:d5cc:e68f(Preferred)
Link-local IPv6 Address . . . . . : fe80::75de:3b4a:fde3:625d%14(Preferred)
IPv4 Address. . . . . . . . . . . : 192.168.0.49(Preferred)
Subnet Mask . . . . . . . . . . . : 255.255.255.0
Lease Obtained. . . . . . . . . . : Saturday, May 11, 2013 11:09:25 AM
Lease Expires . . . . . . . . . . : Sunday, May 12, 2013 11:09:35 AM
Default Gateway . . . . . . . . . : 192.168.0.1
DNS Servers . . . . . . . . . . . : 192.168.0.1
205.171.2.65
NetBIOS over Tcpip. . . . . . . . : Enabled
Here's what we got from the other laptop when it was connected:
Wireless LAN adapter Wi-Fi:
Connection-specific DNS Suffix . : Home
Description . . . . . . . . . . . : Intel(R) WiFi Link 5300 AGN
Physical Address. . . . . . . . . : 00-21-6A-46-2C-CE
DHCP Enabled. . . . . . . . . . . : Yes
Autoconfiguration Enabled . . . . : Yes
IPv6 Address. . . . . . . . . . . : fd00::7d3d:8f84:288:1b(Preferred)
Temporary IPv6 Address. . . . . . : fd00::19d2:9bb7:cb2f:52dc(Preferred)
Link-local IPv6 Address . . . . . : fe80::7d3d:8f84:288:1b%12(Preferred)
IPv4 Address. . . . . . . . . . . : 192.168.0.72(Preferred)
Subnet Mask . . . . . . . . . . . : 255.255.255.0
Lease Obtained. . . . . . . . . . : Friday, May 10, 2013 6:52:20 PM
Lease Expires . . . . . . . . . . : Sunday, May 12, 2013 2:08:25 PM
Default Gateway . . . . . . . . . : 192.168.0.1
DHCP Server . . . . . . . . . . . : 192.168.0.1
DHCPv6 IAID . . . . . . . . . . . : 251666794
DHCPv6 Client DUID. . . . . . . . : 00-01-00-01-18-CF-F4-D8-00-21-6A-46-2C-CE
DNS Servers . . . . . . . . . . . : 192.168.0.1
205.171.2.65
NetBIOS over Tcpip. . . . . . . . : Enabled