Some things to consider about the “problem” computer.
You say it is connected to your server. On what level? just to orchestrator, or is your user connected on a active directory level.
edit: you might not have enough rights to install the package.
First try to install studio and let it run standalone (so no connection to uipath orchestrator). if that works, you can try to connect it to uipath orchestrator.
What does your eventlogs say? (start > eventviewer) then check for application logs.
reinstall your studio by running an elevated command prompt. Direct to the location where you have the msi installer or exe file. And run it from there.
It can happen that your accessrights are simply to “low” to run the robot service.
You can check services (not in task manager), but here: start > run > services.msc and scroll down until you find the uipath robot service.
If it is not running > start it