Tax Year Prior to 2020: Could I claim a new A/C unit that I need to put on my house which was over $4000

Yes, if the unit meets the requirements.  Check the Energy Star Website linked below. 

This is entered in the Deductions & Credits section:

• With your return open, search for energy improvements in the program search box. (Don't search for "energy credit," as this will take you to the wrong place in the program.)
• Click Jump to energy improvements in the search results.
• At the bottom of the Energy-Saving Home Improvements screen, answer Yes and click Continue.
• Follow the on-screen instructions.

If that doesn't work:  Go directly to the Federal Taxes tab, then Deductions & Credits, then Your Home, then scroll to Home Energy Credits.

Tip: You can see which energy-saving home improvements qualify for a federal tax credit at the Energy Star website.

The Residential Energy Efficient Property Credit is what is called a "non-refundable" credit which means it will only reduce your tax liability to zero.  Any remainder can be carried forward to the next year.

This link has more information about the IRS Home Energy Credits .

See below for the various types of Home Energy Credits available.

https://ttlc.intuit.com/replies/3300639