I have tried both methods of entering the diagnostic test. My MacBook Air is a 2015 vintage and should have the intel chip. The fire-vault security is turned off. Can anyone suggest a way forward? Thanks

1 - This post in appearing in macOS 13 Ventura which this computer does not Qualify to run

2 - The Best this computer could run would be macOS 12 Monterey

3 - From the link at the Top Left of this page and I copy and paste and excerpt below

Learn more

On an Intel-based Mac, if you can't start Apple Diagnostics with the D key, try these solutions:

• Press and hold Option-D at startup to use Apple Diagnostics over the internet.
• Make sure that your Mac isn't using a firmware password.

Should above still now work >>

Then have a few suggestions ;

1 - Get Support Choose a product and we’ll find you the best solution.Start now and open an Apple Support Ticket as they are Apple Employees to deal will these types of issues . 

2 - Product Feedback - Apple and make it known to Apple regarding this ongoing issue 

Use FileVault to encrypt your Mac startup disk

Excerpts from above link

Part 1 of 2

FileVault full-disk encryption uses XTS-AES-128 encryption with a 256-bit key to help prevent unauthorized access to the information on your startup disk. 

Turn FileVault on or off

Part 2 of 2

When you turn on FileVault, you can choose how you want to be able to unlock your disk and reset your password in case you ever forget your password.

For example, you can use your iCloud account or use a recovery key. Learn more about these options.

RodG1 wrote:

I have tried both methods of entering the diagnostic test. Pressing "d" on start up and pressing "command d" on start up.

It is Option + D, not Command.

My MacBook Air is a 2015 vintage and should have the intel chip (only requiring "d" on start up. The fire-vault security is turned off. Can anyone suggest a way forward? Thanks

Filevault has no bearing on being able to run the diagnostics.

What happens when you attempt to boot into the online Apple Diagnostics? If there is an error message, then please provide the exact message (picture is best if the message is in English). You need to press & hold the keys immediately after hearing the startup chime. Holding the keys before the startup chime may cause the computer not to recognize the keys (varies...sometimes does not matter). Maybe try a wired external keyboard in case the built-in keyboard has a problem.

What problem are you trying to solve by running the Apple Diagnostics? Most times the diagnostics will not show any problems, plus the trouble running the diagnostics may be related to the other issue you are trying to resolve.

RodG1 wrote:

I was told at the Apple store that we were unable to run diagnostics because the FireValt was on.

I cannot believe an official Apple representative at an Apple Store would say or believe this.

I did not have the password for FireValt

Usually your macOS user login will automatically unlock Filevault. Once in a while this may become separated, but usually only after a password change.

Would you like to share what the real problem you are having with your laptop? The diagnostics most times won't provide you any answers. There are a lot of very knowledgeable regular forum contributors participating on these forums with decades of experience so there is a good chance we can help you. Apple techs/agents don't always have much really detailed real world experience like the contributors on these forums. I can tell you the Apple public documentation is really lacking in many areas, plus Apple does not provide much support for users if third party software is involved.