First thing to check, and it's a common problem, the vacuum hose. The hose splits at the various connection points it the system. Cut the ends off and then wrap the new end in a few laps of electrical tape and reconnect.
No there's no lights.
With the fob battery going flat you then have a few problems but u can over ride the immobiliser with a code entered via the drivers door lock (hassle), all the info is in the owner handbook.
Get yourself a second set of keys and fob it wil save any problems if you carry them also when a longway from home.