A power surge killed my last PC when it ran through my phone line. I now have cable.Can it do the same thing? Do I need to unplug during a storm?

They make surge protectors to run the cable through.

... or consider a wireless modem...

And protection on your power as well, as this is the more likely source of damage due to power surge...

Unplugging during a storm is obviously the best method to insure that a surge will not do any damage.

However, there is products available to protect from surges for power, phone, and CATV. Buy the best you can afford.