In order to traverse on a network, you have to have some form
of source IP address. (your PCs addr, or the internet provider assigned IP addr.)
You can't actually hide completely.
If you buy a router, your PC will be assigned a different IP address
using NAT(network address translation), and although your PC will have a
different address, it will still leave the routers main network port with a
specific or provider assigned address. There has to be a return path for
your data. There will still be a traceable source IP back to you.
If you'd be more specific on why you want to hide the address, someone
may be able to recommend a solution other than trying to hide your IP addr.
EG: a firewall, or VPN software, etc...