It sounds like the skylight might be leaking, but its hard to tell without looking.
If your roof is aging, you might want to have Home Depot At Home Services out for a bid, if they have a store with AtHome in your area.
If you had ice dams, that is another issue.
Most skylight gaskets are only good for 10 or so years, but if it isn't leaking, the flashing around it might have failed.
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