You've probably got object filtering turned on.
As e14softwareuk said,
I see that on your suspect laptop you are running v1.5 and an older version on the other pc.
In V1.5 they introduced these selection filters (so your other PC does not have the filter option), in many cases (during PCB editing) i find them a blessing, but in the beginning i had the same frustration like you when i forgot to check the filter setting.
Have an interesting problem. Well more frustrating...On one of my schematics, I can't select or modify my wires. I can place additional wires but one they are placed, I can't move them or select them. The problem is more bizarre in that if I open the same schematic file from another Laptop running another variant of Circuit Studio, that package has full access to my wires and can select and modify them.
Suspect Laptop running Circuit Studio under Windows 10 is running version 1.5.2 (Build 30)
Laptop running Circuit Studio where wires are selectable is also running Windows 10 running version 1.2.0 (Build 37)
Any advice would be greatly appreciated.