I cant save my part.

Just a guess, but if you're importing from some other system, the file names might be ridiculously long. If you want to save a Creo file, the file name can only be a maximum of 31 characters.

Often when I download models from, for example, SMC, the components in the assembly can have very long names. For whatever reason, Creo is okay with that as long as the part file is bundled into the assembly, but doesn't like it if I try to write the file to disk independent of the assembly. 

Did you ever get it to save?

You don't show enough to diagnose the issue.  What are the latest messages at the bottom of the screen?  What tabs are open at the top?  The more infor you can give, the better we can respond.

My first thought is that you have a process started and still waiting on you to complete.  In the above image, the extrude tab is active and the last message is asking me to do something.  At this point most of the file operations in the menu are grayed out.

Hi 

from your screenshot, we can see Check-in (above Save) which means you are in a Windchill environment.
There are some situations where saving is not permitted indeed.
What message exactly did you have on opening ?

I've not seen this yellow icon before (SOLID48).  This does appear to be an import from perhaps an Autodesk Inventor file.  If it's trying to save back to an Inventor file, that may not be allowed.