1st off Swift, sorry to hear about your misfortune. Really must feel violated and hurt, 'specially if they were a friend at one time.
This same exact scenario just happened to my brother a little while back. Had a loser/scumbag/druggie/freeloading "friend" that entered his home while he was at work and stole ALL of his consoles and most of his games. And yes Iggy, his insurance company paid up. Had simple renters insurance as he rents one side of a duplex. He was quite happy with the claim actually and because he had his receipts for the modern stuff, got most ALL of that value back. Real easy to prove what the older stuff is worth now-a-days thanks to the internet, previous history of sales on ePay, Amibay, Craigslist, wherever.
The Police aren't totally useless when it comes to this... you do need them to fill out a report in order for your insurance claim to get processed. lol They also put A.P.B.'s out for your stuff at places such as pawn shops, music stores that accept trade-ins, etc. It's the single most reason why you need to show I.D. anymore when trading a game in at a retailer here in the States.