How to run a service every day at noon, and on every boot

Android alarmmanager is your answer. use it with a broadcast receiver which also resets the alarms on phone wake.

Now with code example:
Setting alarm inside a method:

Intent intent = new Intent(context, AlarmReceiver.class);
intent.setAction("packagename.ACTION");
PendingIntent pendingIntent = PendingIntent.getBroadcast(context,
            0, intent, PendingIntent.FLAG_CANCEL_CURRENT);
Calendar calendar = Calendar.getInstance();
calendar.setTimeInMillis(System.currentTimeMillis());
        AlarmManager alarm = (AlarmManager) context.getSystemService(Context.ALARM_SERVICE);
alarm.cancel(pendingIntent);
alarm.setRepeating(AlarmManager.RTC_WAKEUP, calendar.getTimeInMillis(), AlarmManager.INTERVAL_DAY, pendingIntent);

Receiver for your interval:

public class AlarmReceiver extends BroadcastReceiver {
private final String SOMEACTION = "packagename.ACTION"; //packagename is com.whatever.www
@Override
public void onReceive(Context context, Intent intent) {
    Time now = new Time();
    now.setToNow();
    String time = FileHandler.timeFormat(now);

    String action = intent.getAction();
    if(SOMEACTION.equals(action)) {
        // here you call a service etc.
    }

Receiver for resetting alarms whenever phone has been shut down.

public class AlarmSetter extends BroadcastReceiver {

    @Override
    public void onReceive(Context context, Intent intent) {
        // get preferences
        SharedPreferences preferences = context.getSharedPreferences("name_of_your_pref", 0);
        Map<String, ?> scheduleData = preferences.getAll();

        // set the schedule time
        if(scheduleData.containsKey("fromHour") && scheduleData.containsKey("toHour")) {
            int fromHour = (Integer) scheduleData.get("fromHour");
            int fromMinute = (Integer) scheduleData.get("fromMinute");

            int toHour = (Integer) scheduleData.get("toHour");
            int toMinute = (Integer) scheduleData.get("toMinute");

            //Do some action
        }
    }

}

Manifest very important, this is added under application:

        <receiver android:name="AlarmReceiver">
        <intent-filter>
            <action android:name="packagename.ACTION"/>
            <action android:name="packagename.ACTION2"/>
        </intent-filter>
    </receiver>

    <receiver android:name="AlarmSetter" >
        <intent-filter>
            <action
                android:name="android.intent.action.BOOT_COMPLETED" />
        </intent-filter>
    </receiver>

Also in order for this to work you need to add permission to receive the boot Broadcast in the manifest with following line:

<uses-permission android:name="android.permission.RECEIVE_BOOT_COMPLETED" />

Hope this cleared things up, if any errors plz tell.

Edit (added alarmsetter example):

public class AlarmSetter extends BroadcastReceiver {

    @Override
    public void onReceive(Context context, Intent intent) {
        // Do your stuff
    }
}