Can I start my prius if fob battery dead?

Your FOB case has probably been changed out at some point in its life and someone failed to switch the rfid chip into the new case.

The OEM case has an rfid chip that is attached to the case cover opposite the side that has all the electronics. When the FOB is inserted into the dash, it disables the wireless SKS and looks for the rfid chip signal. No rfid chip means no rfid signal means the car does nothing.

If that's the only FOB you have then you better keep a fresh supply of 2032s available

 

The RFID chip in the FOB will allow you to start you car if the FOB is dead... The mechanical key will allow you to get into your locked car if FOB is dead. If car won't start with dead FOB, that's a problem not related to the design.

 

When the dash cap(s) fail for good, the vehicle will no longer be able to start, potentially leaving people stranded.

Consider the DIY cap replacement, or the lifetime warranty and updated odometer over at : Prius Speedometer Replacement

 

The rest of your question is already well answered. As for this part:

Those videos were apparently for Gen 3 & newer. They don't have a slot like the Gen 2 so the method is different.

 

It's a tiny little black rectangular block shaped thing roughly 3/8" long... You can reprogram new FOBs to your vehicle using chicken dance but if you program too many FOBs to a car it won't let you add more till you wipe the old ones using a special locksmith feature on techstream that they charge a monthy fee to locksmiths to use. There used to be a service in EU that for ~$40US will do some math with your VIN# that gives you a security key to gain access to that part of techstream, but don't know if they're still around.

 

The chicken dance will only work if you currently have a fully functioning FOB. The working fob has to be used SKS and in the slot as part of the dance.