It doesn't seem to me that your sentence has any grammar mistake but if I were you I would say:It seemed to me (drop that) my car did not have much power; (drop and) then I realized (drop that the) wheels of the/my car were constrained by the parking brakeI am not a native, but with these modification it sounds better. I would like to know a native idea about that. However, I see no mistake.
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exodus74 It seemed to me that my car did not have much power and then I realized that the wheels were constrained by the parking brakeThe sentence is fine grammatically, though it needs a full stop (period) at the end; I would put a comma after 'power'.