If your tv is still within its guarantee period (at least 12 months) then take it back to the shop and request a repair free of charge. Don't try dismantling it.
The Sale of Goods Act makes it the dealer's responsibility to arrange repairs within a reasonable time (that is, you should not have to wait more than a couple of weeks) and they must not make any charge or tell you to arrange it yourself.
If it is out of guarantee then the best thing you can do is to take it to the recycling bank and then buy a new one. This is for two very good reasons:
1) There are no reliable tv/dvd combination units. They are all notoriously unreliable regardless of the manufacturer. The DVD player is usually the first part to fail and they are not user repairable.
2) Logik is one of the family of cheap "brands" which are known to be very unreliable in their own right. These televisions are not built by "proper" tv manufacturers. They are just assembled from low-cost low-quality components and then have a label attached. Other "brands" to avoid include: Alba, Bush, Baird, Beko, Celcus, Goodmans, Grundig, Technika, Tevion, Wharfedale, and any other "supermarket brand".
The best thing for an economical DVD/TV set up is to buy an inexpensive model from a reputable manufacturer such as Sharp (low cost and basic but very reliable) and a separate cheap £30 DVD player from Tesco. The DVD player may last for a couple of years before you have to replace it - and the telly will still be working.