My wife wants me to have a roof built over our stairwell to prevent our basement from flooding. We've lived in our house for 2 and a half years, and the basement has never flooded, but today when we got a torrential downpour, some water was coming under the door. There is a drain at the bottom of the stairwell, but there is bunch of silt in the pipe and a plumber who looked at it said it went to nowhere. Our neighbors had a roof installed over their stairwell and they feel that this has solved their problem. Should I do this? I'm reluctant to do it because it doesn't sound like it fixes the root cause of the problem. What if it's raining sideways and the wind blows rain into the stairwell anyway? What do you think?

3 options I can see. #1 get that pipe to nowhere to run somewhere. I am sure it once went somewhere. #2. Build the roof, sidewalls if you think rain will still get in. #3 install a sump pump with a surface sucking attacnment. Zoeller 42-0007 Floor Sucker Utility Pump - Faucet Depot

I agree with ballengerb1. Get the drain to actually drain somewhere. However, with a very high rate of rainfall and wind, the drain may become plugged with flying leaves etc. Best bet is to completely enclose the stairwell. Roof, sidewalls, maybe even a front with a door. A couple windows for light is always a nice touch. This will ensure no water entering the basement through the stairwell during the nastiest of storms.

If it was my house, I would install sump-pump...

I like to take the cheapest way out that works and rebuilding your house doesn't sound cheap to me. Neither is installing a sump pump.
So that leaves us with bobs door number one.
It's possible to clear a silted line. I know, because I opened up a patio drain for my neighbor last month. If that line's found to terminate in the ground I would build a dry well, (see image) to disperse the water.
Now, didn't that sound better then rebuilding your house? Good luck, Tom