The key points of this query are specified as
I extended my new garden lights using a low voltage cable connector. The "original" was with 7 lights and the "new" is with 3 lights. The 3 (new) lights work and the 7 (original) won't work, even when I remove the extended wire. All connections and bulbs are good. What have I done wrong since I can't even get the (original)7 light to work solo?
It seems that the OP is saying that the new set of lights - attached to the supply at the
end of a previously existing set of lights - is now working BUT, the previously existing set of lights, along the supply to the new lights, is now NOT working !
(Presumably, there has been no change in the connection of the "original" set-up to the supply.)
While the OP states "bulbs are good", the foregoing seems to be completely inexplicable to me - UNLESS somewhere in the set-up process a relatively high voltage has been applied to the "original" 7 lights and they have "blown". I can only suggest that one or more of these original 7 lamps be tested, to see if they are actually still operative, before proceeding any further.