@Dannad Hello, 

 
May I know do you try to set up the range extender using Chromebook? How about the Led Status on RE300 right now. 
On Chromebook Wi-Fi settings, please connect to TPLINK Ext SSID, Wi-Fi status is normally " connected but No Internet"

After that, try to login to range extender by instruction here:
https://www.tp-link.com/support/faq/1408/

If you have difficulty logging into web page, please do a factory reset tp-link range extender : press the reset hole for 10 secs with RE powered on.

If still the same issue, please try to login on your  phone. 
On mobile phone Wi-Fi settings, connect to Range extender Wi-Fi first ( do not connect to router Wi-Fi or and turn off mobile data)

@Dannad Thank you, 

Is there any possibility that RE300 was not successfully set up, as  RE sometimes direct to tp-link management page need set up.  

It is recommended to set up a different name for range extender, and RE300 Wi-Fi & 2.4Ghz & 5Ghz Led should light up. 

https://www.tp-link.com/support/faq/2459/

May I have a photo of the message on your Chromebook, please check what is IP address and gateway when Chromebook connect to RE's Wi-Fi? 

https://www.tp-link.com/support/faq/838/