The drivetrain on my bike needs replacement, given the cost, do I just get a new bike? Probably best to not go through the specific components on my bike, however, the sprockets, chainset, jockey wheels and chain need replacing due to excessive wear. Coupled with that, the cables are in need of replacement too. The rear rim is wearing a bit thin so a new wheel might also be prudent.  

I have done some back of the envelope calculations and the parts bill alone comes to 2/3 the price I paid for the bike originally. Hence, do I just get a new bike? If I do, can I just throw the old one away without any qualms about wasting what is a nice bike, albeit worn out?
I think the appropriate question is not what you paid for the bike, but what it will cost you to replace it. Almost any bike can be repaired (although the grandfathers axe problem also occurs).

I think it's worth doing the quotations yourself. Go over the bike properly and work out which parts need to be replaced, what tools (if any) you will need to buy, and what that will all cost. Then look at the cost of a working second hand or new bike. One advantage of the new(er) bike is that it doesn't have to be the same as your existing bike - if you've been wanting a bigger frame or something the new(er) bike can have that. Of course, a second hand bike will probably also need bits fixed up, which is something to add to the cost.

My expectation is that unless your current bike was fairly good to start with that a new bike will work out cheaper. But if you enjoy working on your bike you should count some of the cost as entertainment (I am building a four poster bed and selling it to my partner this way :)