Slow and steady...
You want your trolls to have claws that were historically used for combat/self defense, but will also allow them to develop a primitive culture. The simplest way to achieve this that I can see is to have them have a larger, stronger version of sloth claws. Sharp claws that curve in and down, perfect for using as a primitive shovel.
Not just any shovel though. We are talking about hulking trolls, so their claws need to be extra impressive. Given their brute strength and claws made of a hyper dense and tough material, you have the perfect recipe for a cave making and dwelling creature. Your trolls would live in mountainous areas or any other location that has natural cave systems. They would then use their shovel claws to dig out new tunnels or expand upon existing ones. Digging would blunt the claws somewhat, but first it would wear away at the curve of the claw. A troll that has spent time shaping his home would have claws that are straighter and sharper. Perfect for defending his new home from intruders.
Once you have a cave dwelling troll, starting a civilization with them is simply a matter of having small groups form and start to cooperate. Maybe multiple troll families live on the same mountain and their tunnels end up running into each other. Or your trolls are naturally more social than typical fantasy ones and they are predisposed to working together. Either way, eventually they will discover the benefits to communal living. One group of trolls could spend their days digging and enhancing the tunnel systems, while another goes out hunting or defending the community. What group a troll is in would depend on the state of their claws. Dig until your shovel claws look like daggers, then hunt/guard until your dagger claws grow back out to shovels.
Once you have a group of creatures living as a community and using primitive tools (in this case claws) you have the everything you need for culture to start to form. Writing and drawing are both pretty obvious, since the stone walls would be perfect for both. Sharpened claws would act in place of knives, so you could have stuff like cured hides for clothing. Assuming they care about things like that. And of course there is the obvious draw to having a race of natural miners when it comes to trade with other creatures. Your trolls wouldn't fill the same role that dwarves do in most fantasy settings, since they will be too primitive to provide processed goods, but they would be a good source for humans or other races to get raw metals and minerals.
Strong arms and curved claws will be the basis for a primitive yet noble cliff-dwelling tribe of mountain trolls.