-2003F recovery error code

<< Resetting the logic board, by holding down shift, control, option and the start button. >>

There is MUCH more subtlety to the process of SMC Reset thant what you have described. Only the keys on the specified side of the keyboard will do the job, and all must be pressed and held in a specific order, as specified in this article. You MUST follow exactly, or nothing happens at all.

Your 2019 MacBook Pro DOES have a T2 chip.

Reset the SMC of your Mac - Apple Support

Hen1den2

"-2003F recovery error code: [...]Anyone know what I can do to overcome the problem?[...]"

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Troubleshooting -2003F Recovery Error Code:

Your macOS is damaged or corrupt. So, in that case reinstall the macOS.

Reinstalling the macOS:

Go Here: How to Reinstall macOS from macOS Recovery - Apple Support. Important: After the install, be certain to create a backup of your Mac prior to all of this. That way, you can have something to restore from the Mac from, should anything go wrong with the reinstall. Once reinstalled, try this once more.

Hen1den2 Said:

"I have repeatedly tried to install Catalina. The Catalina Installer starts, but it is unable to do anything useful."

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Reinstalling the macOS:

I'm saying the reinstall the macOS --the currently-installed macOS will reinstalled --a new macOS will not in installed, and not updates will be made.

<<. Entering Recovery Mode. That never works. After an hour it stops, and this error message shows: -2003F >>

In Internet Recovery, these low negative thousands error messages (between -1000 and -6000) indicate that your provided Wi-Fi Network is inadequate in some fashion, and cannot be used (for this purpose) in its current state.

Common problems include:

Hidden Network-name

required use of a proxy server to get Internet access

required use of a login page to get Internet access

Use of a login server or certificate to get Internet access

Use of PPPoE in the Mac to get Internet access (typically only applies to DSL)

Use of Fixed IP address rather than good old DHCP

Variance of the time by more than five minutes. if your battery has run flat, the time will likely be wonky and have to be specified with a Terminal command

Failure of Router to provide workable DNS server addresses, or providing 0.0.0.0 [may produce -2002f]

If you have an Ethernet port, you may in some cases be able to move your Mac close to the Router and connect to the Router using Ethernet.

The higher the number, the more obscure the problem.