Is this a DNS issue?

[#1]

The current call waiting time for support is 60 minutes, so you guys are my only hope!
I've recently had plusnet installed. Everyone in the house has connected their mobile handsets via wireless, and report no problems, but my laptop is having issues.
Frequently when browsing, I'll find a web page won't load. All further attempts at browsing to other websites fail also. My wireless connection still reports connected, as indeed does the internet status of the connection. To get it working again, I turn off/on the wireless adapter. It works immediately. I don't want to call this a laptop issue, as the problem has only occurred since the switch over from BT.
And the other puzzling thing is, I ran a constant "ping google.com -t" and found no dropouts on the connection, even when I couldn't browse web pages. My gut tells me its a DNS issue. 
Anyone got any advice?

[#2]

Have you tried alternate DNS server(s) to rule in / out your gut instinct
If you have the Thompson router you will need to telnet into the router
Set the router to use OpenDNS  on the R8 Firmware
dns server route list List all DNS resolvers set in the router. ( optional )
dns server route flush Clear
dns server route add dns=208.67.222.222 metric=0 intf=Internet
dns server route add dns=208.67.220.220 metric=0 intf=Internet
dns server route list List all DNS resolvers set in the router.  (just checking)
saveall Make the change permanent.
Set the router to use OpenDNS on the New R10 Firmware
dns server forward dnsset list List all DNS resolvers set in the router. ( optional )
dns server forward dnsset flush Clear
dns server forward dnsset add set=0 dns=208.67.222.222 metric=0 intf=Internet
dns server forward dnsset add set=0 dns=208.67.220.220 metric=0 intf=Internet
dns server forward dnsset list List all DNS resolvers set in the router. 
saveall
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[#3]

Try your laptop connected up with an ethernet cable and try again first!!  Any diagnostic tests to prove/disprove router or Internet issues should always be conducted via a wired connection to cut out the vagaries of wireless performance.