People can DDOS which is distributed denial of service which is basically sending alot of packets to your router and blocks off your service due to overflow. Its almost like when you type in ping google.com in on your CMD but x10000. So yes, they can do something with your IP.
Someone correct me if this is wrong, but:
I think you need to have a program running that is listening for requests and sending out large amounts of data
You can easily stop a DDOS.
Change your mac address.
Some modems might not have a mac address spoofing feature, though?