I've run into the weird problem, where I had to abandon the Prismatic Core quest, and since that time I can't get any fighters guild quests done anymore.
The other day I was at the Earth Forge trying to fight queen whatshername, and eventually gave up after having been beat lots of times. Being a level 28 character against a level 23 queen is something for another thread, though.

OK, so I gave up, logged off, waited 25 minutes and logged back in to find I am at a wayshrine in the world. All fine and good. Played a lot of other stuff, leveled up, and am now at level 32. So I thought, let's try again... but for that you cannot. The portal into the Prismatic Core quest is made at the end of the Dangerous Past quest. We already went through a portal into that quest, and that portal is nowhere to be seen or had, since Guildmaster Sees-all-colors isn't in the same province as I am in, or something like that.
So, for me, I am in the Aldmery Dominion, so the initial portal into the Dangerous Past quest should be in the Fighters Guild room in Elden Root. It isn't. I've been there, waited there for half an hour, nothing happens.
The Dangerous Past quests sits in my Journal as being done. So I cannot revisit it. Or abandon it. Or replay it. Or anything. I can link it in chat, and that's it.
And as such, since the Prismatic Core quests starts from a portal at the end of the Dangerous Past quest, I can't reach that portal as I cannot redo the Dangerous Past quest.
And so, after I'd been to the Fighters Guild HQs in the various cities, messenger Berta Moorsmith approached me when I was close to the FG in Skywatch. Only from there did she give me the message that Sees-all-colors was waiting for me in Marbruk's FG HQ. Shouldn't the messenger just be trying to approach me when I am near or in any FG HQ? And I see that restarts the Dangerous Past quest. Phew.
Jord.
As I burn down and murder, I know that God forgives.
'Spite all the things I've done my soul yet forever lives.
And all those caught in the shadow of my wings have cause to fear.
I swear on all I've done, no evil shall linger here.