Increasing precision of a practical opamp circuit when the input signal is very small
Only the TL084BC has a worst-case input offset of 3mV, and that's only at 25C. (It's 5mV over the full range, and the non-BC versions can go as high as 20mV). Also, the TL084 doesn't have input offset nulling inputs.

Since your signal is swamped by the input offset range of the part, I wouldn't expect good results without some attempt at nulling. There are some methods of external nulling by injecting current, which can introduce noise but may make the opamp useable with such a small input signal.

It would be best to use a chopper-stabilized or precision low offset opamp for such a small signal instead of external nulling, since offset nulling often has a temperature coefficient (depending on the method used).