Debugging SickBeard is a little beyonf the remit of this forum, but I’ll make an educated guess that cron is starting it too early.
If correct, you have a couple of options:
Place your startup command in a wrapper script, that does something along the lines of:
while I can't ping google
sleep 10
done
run Sickbeard
but that’s pretty hacky, IMO.
Since you want it to run at startup, I’d recommend you create a systemd .service file and enable it to run at startup. Here’s a thread about getting SickRage to run at startup:
since they’re related, it should be a good starting point.