How can I be informed through my computer if a new SMS is received?
If you have Android, try Texdro. I tried a few of the other related apps and this worked the best for me. It allows you to send and receive texts from your computer. It also allows you to silence SMS notifications on your phone while the program is running so you can just be notified on your computer (or you can be notified on both). The free version of the app allows you only to connect via WiFi and the Pro version adds USB and Bluetooth options. I will probably be purchasing the pro version when I get some handy $$, mostly to support the dev, because WiFi connectivity works fine for me.

Texdro - Desktop SMS for Android on AppBrain

Android Market QR Code