Why can’t I move the unmanned rocket

Your probe is probably out of power. Unlike manned capsules, probes don't have any internal way of generating their own electricity.* You need to add solar panels (and remember to deploy them once in orbit), or Radioactive Thermal Generators to your probe. Running most chemical engines also generates power (which is how you can get into orbit), but due to limited fuel, this is typically impractical.

If you're using solar panels, you may also want to consider strapping some batteries to your probe as well, especially if they aren't going to be in direct sunlight all the time.

Unfortunately for you, your probe is basically dead. The only way to resurrect it would be to dock something else to it for power generation, but that assumes that a) you have a docking port on the dead probe and b) it's worth it to even do that.

^{*The first part isn't exactly correct, since manned capsules don't actually produce a net amount of electricity, however they don't consume it either, and when you're out of electricity, they still function and now (as of version 0.21) consume electricity when their reaction wheels are used to change orientation.}

Looks like it's a bug! Somehow the wheel motors got disabled. By going around to all of them and clicking disable and then enabling them again, it seems to have cleared out whatever bad state was in there.