You can usually get decent arcs even without grounding, though I really wouldn't recommend it for larger tesla coils. It shouldn't prevent it from operating, though.
I think the problem is with the transformer/capacitor matching, and from there it's just tuning. I would also suggest taking off the topload, or at least putting a breakout point (nail or something else with a semi-sharp edge). Otherwise the charge on the toroid will be dissipated without actually breaking out.