Does spending mana from a dark ritual count toward storm count if replicate is involved?

Storm count is determined by counting the number of spells cast before the current spell in the same turn (CR 702.40a). Spending mana — from Dark Ritual or any other source — is simply an act of paying costs and has no interaction with storm whatsoever. Mana payment is never 'casting a spell.'

When you cast a spell with Storm, the triggered ability counts how many spells were cast before it this turn (CR 702.40b). Each copy created by Storm is put directly onto the stack by the triggered ability — these copies are NOT cast (CR 702.40c), so they do not themselves increase the storm count for any subsequent storm spell.

Replicate (CR 702.57) lets you pay a cost additional times when casting a spell to put copies onto the stack. Like Storm copies, Replicate copies are also not cast — they are created by the resolution of the Replicate triggered ability. Therefore, Replicate copies do not count toward storm either.

Example: You cast Dark Ritual (spell 1), then cast Pyromatics with Replicate paid twice (spell 2 — the original). Pyromatics's Replicate trigger fires, placing 2 copies on the stack. If you then cast a storm spell, the storm count is 2 (Dark Ritual + Pyromatics). The two Replicate copies do not count, because they were never cast.

In summary: only actual cast spells (CR 601.2) increment the storm count. Mana expenditure, Storm copies, and Replicate copies are all irrelevant to the count.