A faulty dimmer switch could produce the problem you describe, so possibly could a failing light switch.
However, a fault such as this needs to be remedied swiftly because it could be a potential fire hazard as the electricity is being restricted in some way which may produce over heating.
Has the wiring elsewhere in the house been altered just before the fault developed? Are there any other clues?
Frankly, this is a most unusual fault which may be difficult to trace without test equipment. Simply replacing parts is just guesswork and may work, but is more likely to result in spending money unnecessarily.
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