I hesitate to put a date on pieces outside of the gulf coast region vernacular pieces I quite familiar with but I will point out a few details. To date a piece you really can't not go by any one detail but rather many parts to the puzzle and to really see the details you need you have to get close and put hands on. Tools marks and joinery, hardware and nail type go a long way to determining the age:
There does not appear to be any plywood however the back appears as though it could be paneling - if it is it could simply be a repair.
From the little I can see of the drawer bottoms it appears they are not ply either.
The dovetails are hand cut - indicative of early or craftsman made pieces.
Notice the joinery. I find the use of nails rather odd - notice the front case work then contrast that with the drawers. It doesn't seem to fit, does it.
So what's my general impression? I do believe it's old-ish. I just can't say how old without documented similar pieces as a reference of style and joinery or without looking for tool marks.
If the back is not paneling but T&G, I would start there, the drawer bottoms and the inside of the carcass to find tool marks. I would be looking for indications of sawing techniques - pit sawing, sash sawing, circle sawing or band sawing. Also the type of tools used to thickness and mark and cut joinery can be indicative of the period.
It is in rough shape - but if it's historically prominent it would be worth repairing.
Jean