I expect your battery has gone dead. (they usually last 2-3 months depending on how often you connect with them) Connecting takes more power than normal- so the 'connection' probably drained the last drop of juice out of your battery. Try the reset button on the back first- if an egg appears - press B - if you get reset/download come on the screen- select DOWNLOAD.
If there is still nothing you need to get a new battery-and when the new egg appears press B and select download.
Tamagotchis don't actually 'go' to other tama's- it's just the computer chip through the Infra red connection telling the other tama what sort of character to show on screen when they connect.
