After an LLC is converted to a C-Corp, are activities conducted by the previous company still associated with the new one?

Are you converting to a corp under state law, or just "checking the box" on the LLC? If converting, its handled under state by state corporate law, but generally the answer is yes. If just checking the box, the entity is the same entity, you are just changing the tax classification. If we are talking about tax items such as losses or audit issues, the answer is generally, no. It was either a partnership and the partners have the income, gain, losses, etc... or it is a disregarded entity and the sole member has the tax items.