How were you set up when firing your groups? i.e, bipod, front sand bags, lead sled, rear bags, etc? Most rifles that shoot randomly at about 3-4 inch groups have some kind of bedding or non-free float issue. If you as a shooter is set up properly (good trigger pull 90 degrees to trigger, not pulling or pushing the trigger sideways, firm shoulder pressure, proper body alignment, etc), then it's most likely the rifle. The 770's that I have seen are not free floated, which will cause the random groups. I don't recall if it's the 770, but one of the lower Rem model rifles are glued in to the stock, and not meant to be taken apart.

If it is not free floated and the stock is making contact with the barrel, and you are using a bipod, then this will put pressure on the action, and cause shots to go random. That's why I suggested free float and a trigger job, and call it good. The 770's can shoot decent (better than the 3"-4" you are getting now for sure), but you have to eliminate the things that can cause randomness.

And if I own a rifle that isn't dead on for a cold bore shot, I won't own it long. You can work through the grouping issues.