well , why not put in a new RTC COIN cell battery?  at 7 years old it is due,, for sure.

we measure them with a  volt meter 2.9 or less bad, 3.3vdc new is par.

or replace it at 5 to 7 years old , slam dunk style.

the service manual covers how to do this on all DELL PCs made at dell.com  for even this exact PC.

I'm not sure what you mean. My computer is 5 not 7. Either way I'm not sure what battery you are talking about. 

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@Bubblet wrote:

Alienware X51 R2. 

1. On startup, it gets all the way to the Alienware logo but then nothing happens, I don't get the animated loading wheel and if I leave it nothing happens the Alienware logo just stays on the screen. If I restart the machine by holding down the start button and turning it back on again, it will start up fine with no issues whatsoever and once started up it runs perfectly with no problems.

2. Is this just a product of its age or is it something that I can fix? 

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1. Try Disabling "Fast Startup" . Then, Force-Disable Hibernation (and be sure hidden Hibernation-file gets deleted).

2. An experienced user or technician would have to make that determination ... usually after some preliminary trouble-shooting and observation.