Does the apple store charge to do a diagnostic test on your computer

You have not said which Mac you have nor its model year, and that is important to your question.. Apple may elect to not evaluate computers they have deemed "vintage" or "obsolete."

Before contacting Apple, see if your device is on this list of devices that Apple no longer services:

Obtaining service for your Apple product after an expired warranty - Apple Support

However..

Depending on what device you have and assuming it is running, you can get a cursory eval here without leaving home. Tell us what sympoms or issues you have encountered. The senior contributors here have accurately diagnosed many people's computer issues without the user ever leaving home. Unlike Apple, we don't worry about what model year you have.

If the computer is running, and if you want a data-driven evaluation in this setting where we can neither see nor touch your computer, please post an EtreCheck report. We can quickly and within the limitations of these forums help you determine what issues are at play without our playing a protracted game of "20 Questions" with you that could go on for days. 

EtreCheck Pro is available here:

https://etrecheck.com/index

The free version will do nicely for this purpose, although the app is worthy of our financial support.

We can see hard data about drive performance, software issues and interferences, and RAM usage. Etrecheck is the development of a long-serving and trusted ASC contributor. It is a reporting app, not a "fix-it” app, expressly for displaying information in these forums to help us help you remotely. It will not reveal any personal or secure information.

We need to see the full post for details, not read a summary. Please see this excellent user tip on how to post long text reports like EtreCheck's into a forum response:

How to use the Add Text Feature When Post… - Apple Community

No. Make an appointment at the Genius Bar.