Ctrl key produces Cmd+Option+Ctrl+Shift

My first thought when I started reading was the same as yours: hardware problem. But just as you said, having the same thing happen with an external keyboard dispels that notion.

Create a new user account (or use the guest account) and test; same problem?

Make an appointment at the Apple Genius Bar for service. If you need to find an Apple Store - Find a Store - Apple. Also, see How to find your nearest Apple Authorized Service Provider (AASP) or Distributor (AAD).

"Your Apple-branded or Beats-branded hardware product (“Product”) is warranted against defects in materials and workmanship for a period of ONE (1) YEAR from the date of original retail purchase (“Warranty Period”) when used in accordance with Apple`s user manuals (refer to www.apple.com/support/country). Under this warranty, you will be able to direct your claims to Apple even in situations where you purchased the Apple Product from a third party.” [Apple One (1) Year Limited Warranty – Accessory - For Apple and Beats Branded Products Only.]

Where is that information in your original post? Talk to your employer or work tech support for help. The computer is under warranty, so let them handle the problem.

Please read Writing an effective Apple Support Communities question. We are here to help. We are all users. We are not mind-readers nor clairvoyants. We only know what you write down and tell us. Be specific and thorough. Include your hardware information and installed version of macOS.

You have 14 days from date of purchase in which to get it replaced or get your money back with no questions asked.

In SystemPreferences->Keyboard->Shortcuts check (and perhaps change) all shortcuts in all chapters on the left side

Please run Etrecheck (from your normal user account that shows the problem) and post its full report here.

Use the “additional text” button and paste the report into the text box.