Thanks for the report, this doesn't look like a security issue, so I'm adding the Profiles component so it can be properly triaged.

--Chrome Identity automated triaging--

This bug is Unconfirmed and has gone two weeks without any activity, so it is being closed as WontFix. Please re-open if this is still a valid and reproducible bug or feature request and mark it as Available. Please see https://goo.gl/78kbny for more details. Please remove the Services>SignIn or UI>Browser>Profiles components if this bug isn't related to Chrome Identity.

For more details visit https://www.chromium.org/issue-tracking/autotriage - Your friendly Sheriffbot

This looks like a general desktop/profiles issue, so re-opening and cc'ing desktop people

dinu.nicolae2004@gmail.com: I missed the original bug, sorry for that. What does it mean "Change the computer and readd chrome settings."? Are you copying over the profile folder from one machine to the other?

Yes, I am copying the profile on a newly installed OS. 
But this happens also with Portable Chrome from PortableApps, when opening it on another PC, rendering it "unportable".

I don't think Portable Chrome is ours, so for support I'd contact PortableApps.

Profiles can't be copied from one machine to another, by design.  If you want your data on another machine, the recommended method is to bring it across using Chrome Sync.

I've replaced the PC and only saved the application data folder. 
How can I retrieve as much as possible from the Chrome profile?

I don't know, honestly.

But somebody must know, since this secure profile thing has been implemented around Chrome 40 version.

I mean, you can try to copy individual files in to the new profile from the old one one at a time and see what works.  But this isn't a case we designed and built for.

Someone from the dev team must know. The problem is that besides losing my credentials to all the online services, as soon as I use the profile on the new PC, it also loses the extensions that were installed. How can I avoid this?

Like I said, I would avoid it by not using anything from the old profile -- anything else can potentially cause problems, such as what you're experiencing.

This isn't a very satisfying answer, but Chrome profiles are meant to be machine-locked and never moved.

This wasn't the case in the past. Chrome auto-updated itself without a single mention of this disaster that followed. 

Updating on the same machine isn't a problem.  You're reporting that you're trying to move a profile directory from one machine to a completely different machine.

Yes, but this "feature" wasn't there in the past. It "arrived" without any prior notice.

What feature?

"secure preferences"