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I guess it's too late to go back to Argos (which would be the easiest / quickest route) but the fitbit warranty runs for 2 years (in the UK) and you can start the process by contacting customer support via: contact.fitbit.com
Have you tried several sources of power e.g. a wall charger used for your phone, as well as a computer?
Fitbit's troubleshooting guide for charging issues is at https://help.fitbit.com/articles/en_US/Help_article/1190/