鍵を求めて机の中を捜した。

key; lock

indicates direct object of action; indicates subject of causative expression; indicates an area traversed; indicates time (period) over which action takes place; indicates point of departure or separation of action; indicates object of desire, like, hate, etc.

to want; to wish for; to request; to demand; to seek; to search for; to pursue (pleasure); to hunt (a job); to purchase; to buy

desk

indicates possessive; nominalizes verbs and adjectives; substitutes for "ga" in subordinate phrases; (at sentence-end, falling tone) indicates a confident conclusion; (at sentence-end) indicates emotional emphasis; (at sentence-end, rising tone) indicates question

inside; in; among; within; center (centre); middle; during; while

to search (for something desired, needed); to look for; to search (for something lost); to seek (a suspect in a crime)