My mother had to replace a modem in her computer after an electrical storm several years ago. However, the damaged modem did not prevent her computer from starting; the modem simply would not work. My mother was not home at the time and the computer was off. It was on a surge protector which also had telephone line protection. But, clearly, a lightning strike somewhere must have affected the telephone line. The surge protector did show signs that it had sustained a hit and we replaced it.
JessicaB, I recommend a UPS (Uninterruptible Power Supply). This is a combination surge protector and battery backup in one unit. They'll protect your computer from power cuts like the one you experienced. If your computer had been on a UPS, it would have continued running during that power drop.
