Question: I deployed a webpart by admin user in Visual Studio 2013 through in SharePoint 2013. 

It's working fine. But when I deploy using another user which already have admin permission then it is showing below error.

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> Error occurred in deployment step 'Retract Solution': Object reference not set to an instance of an object. 
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Answer: 
It's most likely your SpSite or SpWeb object is null because of insufficient rights to the user. Can you make sure that the user have rights on the webapp you are deploying the solution too.
A simple way to make sure that the user have sufficient rights is to create a new test solution and deploy, it will make things clear.
I had same problem and my solution was related with no space in disk for deployment. ps.: database disk.