Short answer : It won't.
Long answer : It can't because there is not enough data being sent to overload the network connection. Considering a lot of PCs have gigabit network cards, flooding a pc with ping requests only sends a few bytes at a time. It wouldn't even be considered a Denial of service attack (DoS)
You would need something like a distributed denial of service attack which utilises many machines which all target 1 particular victim. Better still, an Amplified Distributed denial of service attack using NTP (Network Time Protocol) might do it.
these are considered amplified (or reflected) as you spoof a request which sends a few bytes to a time server, mimicking your intended victim as the source of the request , and it returns many many more bytes to your intended target as a response. Do it to many time servers at once, and you most likely can crash (or at least overload) network connectivity of your intended victim.
See here :
and here :
PS, this is illegal (in some territories), so watch out!