Based on the symptoms described, such as eye pain, blurred vision, headache, purulent discharge, swollen and red eyelid, and inability to move the eye, the most likely diagnosis is orbital cellulitis. Orbital cellulitis is an infection of the tissues surrounding the eye, usually caused by a bacterial infection that spreads from the paranasal sinuses. The symptoms and signs mentioned are consistent with this condition, indicating inflammation and infection in the orbital tissues. Optic neuritis is inflammation of the optic nerve, which does not explain the other symptoms. Papilledema refers to swelling of the optic nerve head, which is not mentioned in the scenario. Ocular trauma and conjunctivitis do not account for the severe symptoms and signs described.