I've never heard of the rice trick before, but if rice does actually act as a moisture absorber it could work. A few little bags of silica gel dessicant would probably be more effective though (you often find them in the boxes that VCRs, TVs, cameras, and similar devices are shipped in).
To really dry out the inside of the phone in any other way you want both warmth and ventilation to carry the moist air away. It can take a long time if you aren't prepared to open the phone up, and damp under the membrane contacts for the buttons might be a recurring problem if it's not dried thoroughly.
If you transfer the SIM card to another phone and it doesn't work immediately, try cleaning the contacts before deciding it's a goner. Soapy water dried on the contacts could be the problem. A rub over with Q-tips dipped in isopropyl alcohol or some similar cleaning agent might restore operation.