Dumb question but have you pressed tv guide on your remote ? i lost ch 4 the other day so i phoned sky and the guy told me its not possible for me to have had ch 4.as its not available in ireland.he basically made me out to be a lier.i hung up and rang again,got a lady who walk me through how to get it back. went into services on remote scrolled down to number 7 and presto,found the channel.
If you want the free-to-air channels only , without a Sky card , then put on Sky News ch 501 , press the red button and before it loads remove the Sky card and press back-up , your box is now programmed with the UK line-up , on free-to air
The list from boards.ie (link below)shows the number for bbc3/4 as 10.773, not 10.733 as you posted - maybe that's why you weren't seeing the channel on the list.
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Channel 4 is included in the general sky entertainment mix package, so there's no need to tune it in under "other channels". Sometimes an individual programme can be blocked because Ch 4 don't have the rights to show it in ROI.