Yes, you can make your own virtual server and it can run from a laptop.
It might not be very fast. I wouldn't recommend an Atom CPU based laptop. Something with dual core like an Asus N would be fine though. Try to have at least 2Gb of RAM on your laptop, so you can give the virtual system 1Gb or so.
First, install SUN VirtualBox (Free at http://www.virtualbox.org) to create the virtual machine. When setting this up there is a Networking option. You can choose from NAT (it can get out but others cant get in), Bridged (asks for a new IP address from your network's DHCP server and is fully on the network for 2-way traffic), or internal network (no internet traffic, internal only -- useful if you have several virtual boxes). The Bridged setting is still fairly safe if your laptop is attached to one of those home networking boxes. You may encounter some issues using wired vs wireless on your laptop. Wired works better.
On the virtual machine, install a Linux of the same flavor as the ISP will use and you will have a virtual linux computer you can play with from under windows.
This won't match exactly, but can get you started.
If you can't find the ISPs linux -- if you want something easy to install, try installing Ubuntu on the virtual box. If you install Ubuntu server edition it has most everything you want already.