Honda Civic LX 2001 Auto transmission issue looking for insight/opinions.
 

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It is hard to say, if it isn't throwing any codes then my guess is you have an internal part problem, ie: clutches, band, or hard parts, gears, drums etc.
A good tranny shop can give you an estimate of what it is going to cost. Find a reputable shop.

Yeah it sounds like the trans is shot, automatic's are pretty weak in these cars, 2001 especially.

Not sure if your model has any switches or solenoid for the gears, but should check on it first.