Possibly downloading the songs IS illegal, but as you have the vinyl nobody would complain as you are right you can have as many backup copies as you like as long as you are not selling, distributing, or playing them publicly (or whatever it is they say).
Incorrect, you are allowed to make one backup from the orginal. As for nobody complaining the Sony EULA that ships with audio CDs (I know :roll:) states that if you lose the original CD (should it be stolen) then you also lose the rights granted to listen to the material contained within. I.e you have to delete your backup. It also stipulates that you lose rights should you become bankrupt or leave the country. There are further requirements stating that it is against the EULA to attempt to circumvent the copy protection systems they have inplace (you're allowed to make a backup, but they have no obligation to make it easy or even possible)
At the moment nobody has been held to the terms of a EULA shipped with an audio CD, and luckily the cases where it has been brought up with regards to software have been thrown out for other reasons. However, all it needs is a precident and suddenly you may find yourself entered into a legal contract for the audacity (no pun intended) of listening to a CD you have paid for.
My opinion is that the record companies should embrace new technology and the culture that surrounds it rather than trying to litigate against it, but that is just my opinion and that doesn't seem to hold much sway in these things. Indeed my opinion rarely counts for anything anywhere :(