* Pouring rain - This is a noun phrase. "Rain" is the noun, and "pouring" is an adjective modifying it.
* has ruined - This is a verb phrase. "Has" is an auxiliary verb, and "ruined" is the main verb.
* your sea-side picnic - This is another noun phrase. "Picnic" is the noun, and "your" and "sea-side" are adjectives modifying it.
* is - This is a verb. It's the verb of the main clause.
There is no conjunction in this sentence. A conjunction connects words, phrases, or clauses. This sentence is a single, independent clause.