I actually think the problem is going to be your router dude and indirectly the hard drive. There is a difference between connecting a device for networked storage and connecting a device for streaming media (different protocols) and the problem here is going to be with your router. Samsung are top notch are there will not be a problem with the tvs. The problem is with the router and what it is trying to achieve. Making the device available to pcs for storage and moving files around is not the same as streaming content to media players whether it be a tv or bluray player. "Standards" exist for compatibility so when you buy different devices and brands you can be reasonably confident they are going to work together. For what you want, you need DLNA certified devices which your Samsung products definitely will be and I can guarantee your Talk Talk router isn't. The reason why I said your hard is indirectly responsible as well is because the hard drive is a vanilla hard drive for storage and at the moment you are depending on the router to manage the sharing/streaming service for you and isp supplied routers simply aren't designed for that.
I respect what you are trying to do as I have done myself for many years and it is fantastic to be able to do is stream tv episodes and movies to any room around the house. You need to do one of two things; either buy a proper 3rd party router like
this or buy yourself a NAS such as
this.
I cannot emphasise enough how much easier your life is going to be if you buy a proper router but I haven't got time to talk about it now (the tennis has started). Suffice to say though that in addition to fulfilling your immediate requirements of being a DLNA certified device, it will offer far more functionality that your current router. If you are happy with what you have got then option No. 2 is the nas. A NAS is a normal hard drive encased in a box which runs it's own operating system and manages the drives and the services it provides. The NAS will be DLNA certified and handle all the connectivity, protocols and everything else and the only thing the router will have to worry about is handling the traffic between the NAS and any device which wants to connect to it (i.e. doing its normal job).
Either option will solve all of your problems and although you might not want to spend any more money I can guarantee that the return on investment will far outweigh the cost. A few years ago I spent just under £1000 on two NAS', multiple routers and switches and running patch cables around the house so every device has a network connection and it is one of the most productive things I have never done. The NAS' are connected to a switch in one room and I send content to the them on a daily basis and family in rooms all around the house just sit back and watch whatever they want whenever they want and everything works seamlessly. All my routers and switches are Linksys and provide excellent performance and reliability, fantastic wireless coverage and obviously handle the wan traffic when the TV's want to go out to the internet and use youtube etc.
I strongly suggest you have good hard thing about how much you are going to use, enjoy and benefit from what you are trying to achieve and then plan your investment proportionally. If you want it to work you are going to have to buy either a NAS OR a new router as a minimum.
If you want any further advice please come back and ask. Sorry for the late response buy I don't check this section of the forum regularly. Now that I have replied hopefully more members will chip in, especially if you want some NAS advice. Many forum members have NAS' and can give you some hands on hints and tips based on their own experiences.