Wifi problems

Install or reinstall the latest wireless driver (from HP's web site for an integrated adapter; else from the adapter manufacturer's site).

How are downloads with an ethernet connection?

What firewall or security suite is, or ever was, on the system?

TCP/IP stack repair options for use with Vista and 7 and 8.

Start - All Programs - Accessories and right click on Command Prompt, select "Run as Administrator" to open a command prompt. [For Windows 8: <Windows Logo> + x - Command Prompt(Admin)]

Reset WINSOCK entries to installation defaults: netsh winsock reset catalog

Reset IPv4 TCP/IP stack to installation defaults. netsh int ipv4 reset reset.log

Reset IPv6 TCP/IP stack to installation defaults. netsh int ipv6 reset reset.log

Reboot the machine.