Sounds like you are talking about a Remington model 8 .
I know the model 8 could be had in 35 Rem.
Renington started making the Model 8 in 1906 I think.
I have not seen 1 for several years but I know of a guy that still deer hunts with a Model 8 in 30 Rem.

I do not know how much it is worth .
Check the aucition sites for a price.