You've said you've worked out that it's LDU604G "OUT 2" that feeds the wall socket in the lounge with Freeview. Is that correct?
Just to double check, if you either switch off the LDU or you unplug the lead connected to OUT 2 then there's no Freeview on the new telly, right?
Next, in the room with the new telly, at the signal wall plate, take the wall plate off the wall. Look at the back of it. If there's any kind of circuit (no matter how rudimentary), or there's a big 'lump' where the downleads from the loft connect to wall plate then its filtered. That will stop the power signal that makes the LNB work. Looking at the LNB on the satellite dish attached to your property, each of the 4 wires/sockets attaches to its own LNB. Each LNB requires its own power feed. In most cases it gets that from the Freesat TV or the Satellite box each of the wires is connected to. If something interrupts that power feed then there'll be no signal from that particular LNB.
So, after looking at the back of the wall plate, what you're looking for is a screw socket on the back of the same style as the OUTs on the LDU604G. These are F connectors. The socket on the wall plate you need should be a simple 'through' connector; basically a threaded barrel connector embedded in to the wall plate and accessible from both sides.
Now take the downlead that you know feeds Freeview to the back of that wall plate. Connect it directly to the back of the through connector for satellite. If you have to remove another cable from that socket before making the new connection then go ahead and do that.
At this point you should have an unfiltered connection from the LDU OUT2 in the loft to the back of the unfiltered Sat connection on the wall plate.
Make a connection from the front of the wall plate SAT connector to the SAT input on the back of the TV. Now go to the loft.
Disconnect the lead from LDU604G OUT2. Take the LNB feed from the dish. Join the two cables together. At this point you now have a direct and unfiltered connection from one of the LNB Feeds from the dish direct to the SAT input on the TV. Once we know you've got all that sorted out, then we can move on to working out of you have a dodgy F connection on one of the wires.
My bet would be the connections from the OUTs on the LDU. You've got blue tape on them. There's no reason for that if the plugs are properly attached to the coax cables. Freeview will scrape by with a crappy connection. Satellite won't. All you need to bugger it up is on single tiny strand of the braid wire touching the centre connector and it's Goodnight Vienna for your power to the LNB.
F connectors aren't difficult to fit, but it's easy to do it messily and end up with no SAT signal. Go have a look at Youtube and watch some videos how to connect the plug. Do the same with yours.