I was sighting-in my .35 Remington today, a 760 GameMaster made
in 1979. This gun was hardly used by its previous owner so its basically
a new gun. Well, I started to shoot and the very first cartridge did not
fire. I waited a few minutes and then opened the action and removed
the shell. The primer was dented, but that's all. In all, I had 10 of these
out of a box of 20. I did get 5-6 fires out of the box. Does this sound
like a bad box of shells or maybe a mechanical malfunction of some
kind? Like I said the gun appears almost brand new so I find it hard
to believe it was the gun's fault. The cartridges were Remington
Core-Lokt 200 gr. soft point. What should I check on the gun to make
sure it is functioning properly?

I would check for old grease hardened in the bolt on the firing pin. Detail strip, clean and lightly oil.

Make sure no WD40 has come in contact with the primers.
Chemicals like WD40 can kill primers. Just a thought. Don

__________________
"Don't worry be happy"

"I would check for old grease hardened in the bolt on the firing pin. Detail strip, clean and lightly oil."

That's where I'd start. The problem is likely with the gun, not the ammo...