Re: My computer is dying... 
Your dream computer description is about as accurate as "I want a black one".
First, since when do computers have terminal cancers where one can predict how long will it live? Even if one component fails, it can be easily replaced.
But alright, skipping past that, getting a new computer. Do you plan on playing newer games on it?
Processor's speed matters incredibly little these days. If you plan on playing some new games, importance of components changes to -
Graphics card,
Power supply,
Processor, mother board, RAM,
The rest.
Any processor on the market currently will do. Seriously, you have to search specifically for the oldest processor in stock to find something NOT worth getting.
Your average middle class CPU will do just fine.
GPU is where magic happens - faster graphics card - more FPS. Except for very few specific games which require heavily on CPU power (thus, having sh*tty performance on most gaming systems where other games slide).
Power supply is one of most important components, one of few most prone to failures. Good PSU and motherboard is what keep your computer running for ages.
Rest is pretty much "to taste". Or budget.
Best you can do is buy all the components seperate, then assemble them together. Reason is that pre-assembled computers often have some components which do not sell all that well (surprise, huh?), so people not very knowledgeable in computers buy it anyway.
Pre-assembled computers also (in my experience) cost more than if you assembled that exact system down to a component yourself.
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