that you bought this machine, but in general terms you are entitled to expect that the power socket pin will not break from its connection on the motherboard during normal use.
Forget this "force of nature" phrase - It's meaningless, and I certainly have never heard it before. I suspect that what the Time Customer service person was saying was "Force Majeure". This is a commonly used legal phrase which, literally translated means "Greater force", and is normally applied to what you and everyone else might call 'Acts of God' or other disasters beyond your control.
The pertinent fact here is that a power connector will not fail in this way in normal use, and you have every reason to expect Time to repair the fault at their expense. Failing that, you can expect a replacement machine. It's up to Time to pay for collection and delivery of the machine, and to return it to you in a fully repaired state within a 'reasonable' time.
Remind them of that, and do it in writing, by special delivery.
I'm basing these comments on my assumption that you haven't had the computer for that long a time.