Power surges frequently cause modems to fail. The most common cause is a surge through the telephone cable during a thunderstorm but mains power surges are also known to cause problems.
The only solution is a new modem. They're cheap and fairly easy to fit but, if you don't feel confident doing it, please DON'T go to somewhere like PC World (who charge an arm and a leg for fitting their over-priced modems). Just look for a local independent computer repairer who'll almost certainly be far cheaper. (The alternative is to buy an external modem - which is what I use. Then you won't have to bother about fitting it yourself or paying for someone else to do it).
Firms such as AUT Direct sell internal modems for �5.99 and external modems for �13.99 - p&p extra. (www.autdirect.co.uk, 01702 382740)
The above assumes that you're using dial-up. If you're on broadband, you'll still need to get a new (broadband) modem but it might be worth asking your ISP whether they can supply one cheaply.
You should be able to reclaim the cost of a new modem (including fitting, if required) from your electricity supply company but you might face an uphill task.
Chris