Sounds like they are too dry!

What is your watering regime?

I agree with Teegee. Orchids need to be flushed through with water every week, after watering leave them to drain for a few minutes, feed with orchid fertilizer every week. In the winter water them only every two weeks. Rain water is best.

Agree with Chino, if you have a water butt, use a jug and flush the water through the pot and over the leaves. You can get little tubes of feed at GC checkouts and pop a few drops in when you have drained them. If you wait they send out a budding stem and perhaps start a new leaf and a couple of new root shoots too. So flowering is not the only activity your plants want to do. If you cut just above the leaf axil below the failed buds, you might get a shoot from there that will flower.

I agreewith all the above but wonder if the windowsill is the ideal spot, mine are not in direct sunlight and temperatures on a windowsill can get very hot or very cold.

Just to add to what the others have said;

It might be worthwhile spraying the buds/stems with clean water this will increase humidity around the buds and perhaps soften the buds a little, thus allowing them to open.

But do not overdo it as too much can create other problems.

I am only suggesting this as a one off task to soften the buds a little.

BTW I am assuming you have Paleanopsis, this link might help.

http://www.thegardenersalmanac.co.uk/Data/Cymbidium&%20Orchids/Cymbidiums%20&%20Orchids.htm