Recombinant protein has been shipped in transit for several weeks, and the ice/blue ice packs have melted when package been received, can the protein still be used in experiment?

Proteins as lyophilized form are relatively stable and can be used in experiment as normal. 

Proteins as frozen liquid form need to be tested before use. It is recommended to perform an SDS-PAGE test to confirm the condition of protein. If the protein is not degraded, and the purity and concentration meet the specifications, the protein can be used in experiment.