Additionally, your description of a DDOS attack is wrong.
A DDOS attack occurs when large numbers of machines at varying locations in the world all attempt to communicate with a very small number of machines (possibly only one) located in one place. And, they don't do it with "ping" packets. One of the things that makes DDOS attacks extremely hard to protect against is the fact that legitimate traffic and attack traffic is generally indistinguishable from each other. In order for the traffic to "look the same", the communications must look the same - this means that these distributed attacking hosts would all be sending a SYN packet or possibly attempting to complete the threeway handshake (SYN - ACK/SYN - ACK) in massive quantities. Ping packets use an entirely different protocol and have no concept of connections, SYN, handshaking, or anything else that has to do with legitimate traffic.
The premise behind a DDOS attack is to "flood" the receiving network, firewall, server, etc. with traffic that -seems- legitimate, making it almost impossible for traffic coming from legitimate clients to operate. If the target is a web site, it can disrupt its operation and cause financial damage to the company that runs it.