As suggested - DO NOT put the modem behind the TV or even close to it. There is a good chance there will be a lot of noise from the TV, DVD player &c and that could affect the signal.
I would put the master as close to the incoming point as possible and the modem close by. Then Cat5e to the various pints around the house.
As you are new in to the property the BT Tech should have no problems in installing a new master where you want it. As for the junction boxes, provided they are standard ones - keep hold of them them may be useful in the future.
M H C
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