I have a few suggestions, but their applicability will depend on the rest of your setting:
1. How it's found: If the previous wielder used it to escape a trap, this would justify it laying dormant for hundreds of years (particularly if the wielder was only partially successful.
Example: <PERSON> is at a local temple when there's a massive rumbling through the floor. The clerics unseal the entrance to the abandoned catacombs beneath the temple, and send <PERSON> down to investigate. Down there, he discovers a room filled with stone rubble, and a plain wooden staff jutting up, unscathed.
The room had had a "collapsing ceiling" trap (<PERSON> style) which had been triggered by some adventurer centuries ago. The adventurer had used the apparently-unbreakable staff to hold up the ceiling, and had either escaped or starved. 300
After hundreds of years of focusing all its weight on a single point of wood, the stone slab of the ceiling had finally cracked and collapsed to either side of the staff. If the area is humid, the fact that the staff is still in perfect condition (the metal caps would be free of rust) would also indicate that it's not a mundane item.
2. What it does: When wielding the staff, NotBilly wouldn't feel any different, but he'd wind up using the staff almost as an extension of his body, even if he had no training with such weapons.
If he trips over a root, he darts the tip of the staff out to brace himself and maintain his footing without breaking his pace.
If someone throws a rock at him, even if it's from a direction he can't see, the he whips the staff around to block it (maybe not necessarily successfully every time). Maybe he even bats it directly back at the thrower.
If someone swings a sword at him, he blocks it with the staff, and it makes a sound like you'd expect from a steel blade impacting wood...but the staff remains unscathed.
When he tries to hit someone with the metal ends of the staff, he seems to always find just the right spot: maybe he clocks them in the elbow and makes them drop their weapon, or slips through their guard and stuns them with a blow to the head.
3. The weapon is special, not the wielder: You could also illustrate the weapons capabilities by taking it away from <PERSON> (perhaps a villain steals it while the hero sleeps, or replaces it with a mundane staff), and NotBilly loses the capabilities to which he's grown accustom...and the villain gains those capabilities until the weapon can be retrieved. 300