The ISP would deny responsibility even if the phone line was on fire...
Bunch of questions:
- Does this also occur when both the desktop and the laptop are turned off?
- What DNS server and router settings was your iPad given? (Settings > WiFi > tap the circle-i next to the network you're connected to)
- Is there proxy server configured on the iPad? (same screen, further down)
- When you got your new iPad, did you try browsing before restoring from iCloud/iTunes backup, or only afterwards? Can you try browsing from a factory clean install (set up as new iPad)?
- Can you check whether there are other WiFi clients connected to your router?