Enceladus
2 Iron

Re: Inspiron Duo docking station wont play BBC iPlayer or 4oD

Right click on the video when it is playing. Then select "Settings" and then uncheck the tickbox for "Enable hardware acceleration". (In the Display section which is the first one to show.)

Should have nothing to do with your issue, however it seems to be a cure-all for a host of Flash player bugs.