It's not so much broken, but I can't tell you how frustrated I am about the fact my mum borrowed my phone for 1 day and managed to lose it. We know it's in the house because she didn't go anywhere else at all. But I was wondering if there was some kind of 'remote' way of turning a phone on, so then I can ring it and find it. We've searched the house literally everywhere, we even had a massive clearout and went under the beds, in the attic and everywhere.. so it would be a great help if i could just turn on my phone so I can hear it ring and find it. It's been missing for 3 weeks now.. and my add ons, texts and internet are going to expire in 10 days :(
Sorry, bad news. You can't turn it on remotely. There are indeed stories of the FBI bugging people using cellphones that are supposed to be off, but to do that, they had to install special software first - and they had to do it while the phone was on. You'll have to accept that the phone is totally and completely OFF and there's nothing you can do about it.
Now, about finding it.
You've clearly tried the "space based" approach to location. You go around the available space (her house) identifying places which are large enough to contain the object, and you check them. This is a natural approach, and works well for large objects that can only be contained in a small number of places. It doesn't work so well for cellphones. They're too small.
Try a node-based approach to where it might be. Make her carry a real object. Preferably a cellphone sized one, that she'd like to put down. Now think of her house in terms of nodes (identifiable PLACES such as standing by the kettle, sitting by the fire) and nets - ways to get from one node to another. Ignore the nets - she wouldn't have put the phone down while walking from A to B. Focus on the nodes. Make her occupy each node in turn, and don't pressure her... make her think about where she might put it. And seriously, make her carry something - you'd be surprised how automatic putting something down might be. When faced with it, she might even REMEMBER where she put it.
Now, for each place that she identifies; consider how the phone might become lost. Is there a place where it might slip away? Down the side of a sofa is an obvious one, but you probably thought of that. Be creative. Did she make the bed over the top of it? Did she put it down in, or on, something that moved, or got put away? A purse, magazine rack, scrapbooking folder? Whatever she has. Ask her what activities she did that day, too. Separate 'activity' from 'place'. Make HER think of the activity, while YOU consider any kind of associated container that might have been put away with the phone inside.
Pay special attention to clothing, and purses/handbags. I have many times 'lost' items because I keep it "in my coat" and I check "in my coat" and fail to find it... because it's a different coat. If she says she "checked her purse" - ask her to check the other purses. We tend to think of "my coat" and "my purse" as a single concept - but it's more than a single hiding place to a cellphone.
Take $100 with you when you visit her, and tell her to look after it because you don't want it on you when you go shopping. Watch where she puts it! You can say "just kidding" at this point, but check around that area to see if she put your valuable cellphone in the same (or similar) place.
Finally, the outlandish suggestions. Are there any similar cellphones in the family? Just think - if you have a sister, she might have visited, seen the cellphone, and knowing full well that *********** doesn't have one, assumed that it was hers, and taken it away. Any kids in the family? It's not really stealing to just move something from the kitchen table to the toy box - especially if it looks like a neat toy and has games on it.
That's it from Bad News Guy - good luck with it.