Lightroom does not start because of not being able to connect to server

Hi All,

I hope you can help me, as I start to get desperate...

Upon starting Lightroom Classic CC, it either crashes and hangs itself and does not do anything or it says it could not connect to the server to authenticate me (I have tried a million restarts already). I never had this problem before, it was working all fine so long. My internet connection is fine, I checked the system time and the time zone, also all fine. Also my subscription is fine, just also checked the payments.

When I ping the activate server (https://activate.adobe.com/servlets/ping) I get back the "pong", so all looks good. However, as I understand this is used by older LR versions only.

When I ping the other activate server, used by the up-to-date versions, and I guess also by my lightroom, https://lm.licenses.adobe.com/vact/ping, I get back "400 Bad request Request Header Or Cookie Too Large"... So obvisously I cannot connect -- and I have zero idea why not!!

Please someone, help me!

Many thanks!

Ani