What volts can I supply the VBAT pin with?

So I checked it over extensively and here is where I am at. I have a NRF905 connected exactly as follows:

var data, csn = B10, dr = B1, txen = A6, ce = A7;
SPI2.setup({sck:B13, miso:B14, mosi:B15});
var nrf = require("NRF905").connect(SPI2,csn,dr,tx­en,ce);
var myAddress = 0x17;
var masterAddress = 0x27;

function rx_callback(data){
  console.log("got "+JSON.stringify(data));
}

E.on('init', function() {
  clearWatch();
  clearTimeout();
  nrf.init(myAddress, rx_callback);
});

save();

When I have the PICO connected to the NRF905 with the computer powering everything works fine. When it is connected to the the battery without the NRF905 I can still talk to it with the computer. When connected with the battery and NRF905 then all connection is lost and am unable to reconnect. The pico led blinks very fast.

The pins seem to read as follows (connected to computer only, or connected to battery without NRF905):
Bat in is 13V, B15 is 3.3v, B14 is floating, B13 is 0v, B10 is 3.3v, B1 is floating, A7 is 3.3, A6 is 0v, A5 is floating.

With the battery they are similar but seem to be resetting over and over.

GND is 0v, VBAT is 13V, VDD is 3.3v, B3 is floating, B4 is floating, B5-A8 are 0v.

I do have an oscilloscope but its currently not working properly..... And not sure where to even begin even if it were working......