If the new computer has WiFi built in (like all laptops) you don't need a separate WiFi card. No guarantee for the signal strength received (how many bars) and the speed.

If the distance to your router is too big to have a strong signal, possible solutions are:
- move the router to some place in the middle of the house
- try a wireless extender
- use an Ethernet cable to the router
- use powerline Ethernet
- use a better antenna then the one bult into the all-in-one

Kees