From the symptoms I think your Sky box is faulty. If the channels have disappeared on the Sky box the TiVo won't be able to record them. One common cause for this sort of behaviour is a failing power supply in the Sky box.
You will have to get the Sky box working properly. First try unplugging the Sky box from the mains for a few minutes and see if that helps. You could also try without the viewing card - you will lose the regional stations but see if you get BBC1 London on 101.
If that doesn't get the channels in the right numbers on the Sky box you could look at a replacement Sky box from ebay. Alternatively you could try a repair using a kit from Satcure
http://www.satcure.co.uk/accs/page12.htm#grundigkits but that is a bit of a gamble as it may not be the power supply.