Can you steam clean your range hood, by adding dishwashing liquid to boiling distilled water?
Clogged? Failing to suck out fumes? Quantitatively, how bad is it? And in what manner did this situation arise? Slowly, over time? Or suddenly? Can you hear a fan running?
Grease has a high boiling point, and while it is theoretically possible to clog some fine filter, it is doubtful that 4 years of home cooking could stop a hood fan from operating. In commercial practice, hoods over grills are cleaned frequently from spattered grease, not so much for better air flow, but more for sanitation and prevention of possible fires from leaping flames.
If no filter is accessible from the stove end, perhaps the exit end is the cause for blockage. Exit openings frequently have flaps to prevent rain entry. Two possibilities: 1) the flap is stuck down and hinders airflow, or 2) the flap is stuck up and the tube is blocked by a bird nest or a pile of acorns. (Of course, this exit end will be so high that it is not accessible for cleaning, but that's another problem.)
There is a third situation. In my former house, the builders omitted an outdoor exit pipe for the microwave and fume hood. There was simply a fan which sucked the steam/vapor up off the stove, thru the filter and back at the cook. We generally turned the fan off. The idea of a fume hood was nice, but not really necessary.