Wifi connected but no internet access via iMac (PC okay)

[#1]

Could anyone please advise on the following. Been using an iMac for a few months via PlusNet Fibre without problems - side by side with an older PC running Windows 7 (also without problems). Suddenly today the iMac won't give me access via the internet i.e. pages won't load or just very occasionally - happens on both Safari and Chrome browsers. Wifi connection is fine. Same with Mail - won't sync but then get the odd one come through but later than the PC.
Looking through some Apple help pages there seem to be similar problems over time - internet access stops, wifi still connected etc. but a lot of the solutions appear contradictory. Mention of changing DNS settings - the only thing I could find on PlusNet help pages for Macs was to add DNS settings of:
212.159.13.49 and 212.159.13.50 although this is from 2011 Plusnet help page so not sure if still current. Added that to the existing 192.168.x.xxx settings but still to no avail. Have re-booted iMac and rooter to no avail.
The Windows PC internet access (also via wifi) working fine - typing this on it.
iMac running OS 10.8.5 - haven't upgraded to Maverick yet.
So any thoughts please?

[#2]

Update - gave up tinkering and probably made matters worse! So deleted the PlusNet network on the iMac - well tried to but it seemed still to be listed?
Anyway, used an Ethernet cable to connect the router directly to the iMac and that restored the connection immediately. So that might normally imply a wifi problem but as previously said the iMac indicated wifi was connected correctly and it was working fine with a PC (and an IPad and Windows phone) and still is, so don't think it was the problem.
Will disconnect the cable and retry wifi again later - but cable can probably stay anyway.

[#3]

I have seen the like of this before with the TG582n router - some devices work OK, others do not.
Symptons are that you have a conenction to the WiFi infrastructure but no internet access (or indeed to anything on the LAN - e.g. the router) because the host has no IP address.  Can you determine the IP address the iMac thinks it has when WiFi connected?
I have been trying to get more insight into the issue with PN.  It rather looks like the DHCP lease allocation message process does not ensure end to end successful delivery, so that if the WiFi signal is marginal, the host does not get the DHCP address allocation.
Connection via ethernet successfully acquires the DHCP address allocation and thus internet connectivity is not a problem.

[#4]

Quote from: Townman

…..  Can you determine the IP address the iMac thinks it has when WiFi connected?…..

Not sure what I'm looking for yet - still trying to find my way around the iMac (how's that for a confession) - will update this as and when I find it! Thanks

[#5]

Should be in the Settings app under Network, Airport or Ethernet depending on which you're using.
Also as an aside you should put the PlusNet DNS servers before the 192.168.***.*** entry, for the iMac to use them before trying the router's DNS pass through setup.