... and I don't have freedom of movement cast on me right now.
I do, however, have the ability to cast any spell I know as if it had silent spell and still spell attached to it, without increasing the caster level.
If I cast a spell with components: V, S ... what happens?
You have to make a DC20 + spell level Concentration check to cast the spell: see the Concentration skill in the PHB...
SRD said:
Concentration DC 20: Grappling or pinned. (You can cast only spells without somatic components for which you have any required material component in hand.)
1 If you are trying to cast, concentrate on, or direct a spell when the distraction occurs, add the level of the spell to the indicated DC.
If you're casting the spell stilled, it has no somatic components...
SRD said:
Benefit: A stilled spell can be cast with no somatic components.
If you're grappled by Black Tentacles, you're still able to speak, so - as akbearfoot said - you don't need to worry about it being Silent. Only
pinned characters can be prevented from speaking, and the Black Tentacles spell won't pin you.
SRD said:
Once the tentacles grapple an opponent, they may make a grapple check each round on your turn to deal 1d6+4 points of bludgeoning damage. The tentacles continue to crush the opponent until the spell ends or the opponent escapes.
Nothing in there about them doing anything other than crushing you to a pulp.
Does it turn into a spell-like ability?
No, absolutely not. Spell-like abilities don't require material components, for one thing. A Stilled, Silent spell that still has a material component requires you to have the component in hand or you can't use it whilst grappled. A DM might well allow you to make a grapple check to withdraw a spell component from a pouch, but - if you succeed - you can't then cast the spell until next round.
You also can't cast a spell with a casting time of longer than a standard action whilst being grappled: it's not
harder, you just "can't". This is important for spontaneous casters: applying metamagic to a spontaneous spell - making a spell Stilled, for instance - is a full-round action, meaning that it can't be cast in a grapple.
You said that you can cast spells "without increasing the caster level", (I assume you actually mean "without increasing the level of the spell"), but can you do it without increasing the casting
time? If not, you're limited to verbal-only spells.
Can anything (like grappling, or being paralyzed) stop me from casting this spell that now lacks components for me?
Yes, you can fail a Concentration check due to being grappled or taking damage during spellcasting. Someone could still disrupt your casting with an attack or spell: counter-intuitive though it may seem, there's no reason why someone couldn't ready an action to disrupt a Stilled, Silent spell you're casting, even though it has no components.
Also, can anyone point out what book & page I should look at for clarification on this particular D&D rule?
If only there were a particular D&D rule! You need to check the grapple rules, the Concentration skill, the Still Spell and Silent Spell feats and the general rules about spellcasting.
The Rules Compendium has this to say on the subject of spellcasting whilst grappled:
"Cast a Spell: You can attempt to cast a spell while grappling or pinned, provided its casting time is no more than 1 standard action, it has no somatic component, and you have in hand any material components or focuses you might need. Any spell that requires precise and careful action is impossible to cast while grappling or pinned. If the spell is one that you can cast while grappling, you must succeed on a Concentration check (DC 20 + spell level) or lose the spell. You don’t have to make a grapple check to cast the spell, but it takes its normal casting time to cast."
Hopefully, all your bases are now covered
