Disclaimer: This bug has already been solved, by myself. Posting here, in case somebody encounters similar issue.
TLDR: Don’t run EVE if you are low on drive space…
So, me and my wife are both playing EVE (finally convinced her after years of her just watching me play, yay!). We use different user accounts on our PC to separate personal stuff, but some things are shared - like EVE instalation folder, for example…
Today she got to PC before me, and wanted to check EVE, for daily rewards (she is still within new account period) and to run some missions (currently doing SOE Epic Arc).
Unfortunately, I have installed some new utility programs yesterday, which decreased avaiable space on drive significantly (seriously, Windows? 6.8 GB of free space is still “too low”? 
I can remember, when I had to work with tens of MBs, not hundreds of GBs… - I am old, it seems).
So, when she started launcher, it began updating client - and then promptly failed while copying downloaded files. Drive space completly filled.
She moved some folders to external drive to free some space, and then resumed patching.
Everything seemed normal, until she tried to login.
She succesfully got to character selection screen. But there everything was grayed out and unclickable (except NES - go figure…), one character even completly missing (except small red X), and daily login reward window didn’t show up.
She tried quitting EVE and re-logging multiple times (unsuccesfully), before she finally gave up, and called me for help.
To verify issue, I switched to my own PC account, and launched my own client.
This time no update occured (shared EVE folder, remember?), and I succesfully logged in, and launched my charcter.
Then I got this…
See that strange thing in middle? It’s station interior, zoomed out(side)…
Ok, so I tried relog(s) too, but no success. At least, untill I remembered - cache files!
So I went to settings, cache files, verify. Over 8000 corrupted files found…
And voila, solved (for both of us, we tried it)…
Only thing I regret is not taking more screenshots - our normal view from inside doesn’t show station interior enough, as our camera is confined to (relatively) small sphere around our ships…
So, again. Moral of this?
Don’t run EVE (or at least update), if you are low on drive space…
Fly safe!