You can short cut some steps to save time. If the TV has a "Digital only" tuning option, then use that. There are no channels broadcast in analogue any more.
Okay, you say you bought a new aerial and connection cable. But you haven't given any details about what kind of aerial (indoor / outdoor - DIY or professionally installed); my guess is that it isn't a professionally installed aerial because the installer would have tuned the TV and checked the channels. That's what I do for clients when installing. So that suggests a DIY install or an indoor aerial. This is where I think your problem might be.
Indoor aerials aren't that good, especially for Freeview. Part of the problem is they're not particularly efficient despite the sales blurb promises of ultra high gain and built-in amplifiers and boosters.... They're just a bit crap unless the house is in a very strong signal area. The second issue is location. If the aerial is in the opposite side of the building to the direction of the TV transmitter mast then the walls in the property will block the signal.
Third, it's orientation of the aerial. If you look at your neighbours roof aerials you'll see that they're all pointing in roughly the same direction, and that they're all aligned either horizontally or vertically. What I mean by that is the little vanes along the spine of the aerial can either be parallel with the ground, or they're at a 90 degree angle. This tells me as an aerial installer if the local transmitter is a main mast or if it is a repeater station covering an area where signal from the main transmitter is weak. Whatever aerial you've bought needs to be aligned in the same way, both for direction and for orientation.
To have much hope of getting a successful Freeview tune then you have to get the aerial pointing and aligned correctly first before trying to tune. The old "analogue" idea of waving the aerial around to pick up a station won't work. Freeview is a digital signal. If the aerial isn't in roughly the correct position before you start then you'll get nothing; simple as that.
You're going to have to do a little bit of homework before you can properly attempt to align the aerial and tune the TV.
Start HERE and put your postcode in to the search box to find your local transmitter: http://www.ukfree.tv/transmitters.php
When you've got your transmitter, go click on the box " Full details " (same line as 'Mapping details' and 'Terrain plot') and this will give you a list of the channel numbers e.g C49, C57 that you should get a signal on. The C numbers isn't the TV channel like you press 101 for BBC1. It's the tuning channel that corresponds with a frequency. When you go in to the TVs tuning menu, and then see it counting up through the channel numbers, that's what this is.
What you need to do next is choose the C number for the BBCA or Com D3+4, then manually tune the TV to one of these. Now, with the TV ready to receive one of the strongest transmitter frequencies for your local area, you'll be able to tell if this aerial you bought has a hope in hell of receiving anything. Point your aerial in the same direction as your neighbours roof aerials. if you get it in the right direction then the TV should start to pick up channels.
Many TVs have a way to display Signal Quality and Signal Strength. Check your manual. By far the most important is Signal Quality. You're looking for 80-100% on this scale. Signal Strength is far less important. You need as little as 40% on this scale for Freeview to work. The problem with indoor booster aerials is they're all about Signal Strength and not Signal Quality.
Once your aerial is set you can try a full tune. It may require some tweaking to get the weaker channel groups (Muxes), so be patient. But if you haven't got any further after 20 minutes then chances are your aerial can't pick up much more. Extra boosters won't help. All they'll do is make a poor weak signal in to a poor stronger signal. They won't improve the Quality. You need a better aerial or a position outside with some height with direct line of sight to the transmitter to get better quality.
Indoor aerials work better near a window so long as the window faces towards the transmitter.
Finally, ignore what's written in customer reviews from retail sites. Just because a certain aerial worked well for some people doesn't mean it will work well for everyone. Each location presents its own challenges.
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