Unless your carabiners, cams or nuts are corroded, and it doesn't sound as if they are, they are as solid as the day you put them in hibernation. The only problem you might have is dealing with the laughter at the crag when you whip out your museum pieces. Gear has evolved a lot in 10 years and your gear will be heavy and clunky compared to what's available today. Imagine a Flintstone's mobile next to a Honda hybrid and you get my drift. But your gear should work perfectly fine.

Your ropes are another matter. Maybe they are OK, but there's no real way to know, short of strapping them into a drop-test tower and breaking them to determine their strength loss over time. Since there isn't a single recorded instance of a rope ever breaking due to just being old, I'd feel comfortable climbing on your cords. The greater consideration is whether they might have been exposed to chemicals such as battery acid, which are real rope killers and common in a garage-storage situation, and/or wear. Cut up and throw away any rope that might have been contaminated, and run both ropes through your hands to feel for soft spots or other irregularities like bite marks from critters. You said that one of the ropes was barely used and neither had held big falls, so I suspect you are good to go with them.

Bear in mind that those 50-meter ropes, while the standard back in the day, will be too short to lower from the anchors on the newer routes established with 60- or even 70-meter lines. I'd relegate them to toproping and fixing, and get lighter and trimmer modern cords, 10mm or just under and at least 60 meters, for leading.