That PC looks like it has the specs to do photo editing without too much trouble. 🙂
If your old LR still works, I’d keep using it. I haven’t found anything better than LR (mostly because I’m so happy with LR that I haven’t looked too hard. 🙂 ) RawTherapee is a free alternative with a learning curve if you’re interested. Affinity Photo is a one-time purchase, and it can do RAW editing, but it’s not really optimized for mass photo editing and sorting like LR is. AFF Photo is basically a direct Photoshop replacement (and a whole lot cheaper!) Highly recommended if you need an alternative to renting PS.