What is the difference between the following:
Things started to work again.
Things started working again.
In many cases — and this is one of them — there is no difference between start with an Equi (PDF) infinitive complement clause to work again in
and start with an Equi gerund complement clause working again in
Some people sometimes might use this distinction in form to signal a distinction in intention or use, but only under special circumstances. Other people might ignore it.
One distinction it might be used to signal is that between continuous and intermittent. If I were describing recovery in a town after an electricity blackout, I might use Things started working again if there was sporadic recovery and Things started to work again if the recovery were genuine.
But that's really just me. In other cases it's clearer.
Either one might be used for an artist/author/etc. who had endured a dry spell and gotten past it. But it's the second one I'd use to imply that he has a new job.
In this case, there is no difference (unless you want to do some heavy hair-splitting), but you have to be careful. A standard counterexample is, “He stopped to eat.” versus “He stopped eating.”.
Think about this:
I'm going to shop.
I'm going shopping.
In term of the information communicated, they are equal.
However, there is a tangible difference in attitude and focus.
I love to ski.
I love skiing.
Generally, the gerund form of the verb highlights the activity as a process, something in progress. This is why some refer to the "progressive" rather than the "continuous" form.
In highlighting the activity as an ongoing process, we may be communicating an emotional attitude.
Think of the McDonald's slogan:
I'm loving it.
Now, contrast that with a possible, and probably more grammatically correct:
I love it.
As living beings - Life is for (the) Living - we have a special emotional connection to the gerund form of the verb that is simply not present in the declarative infinitive.
To be is certainly not the same as being.
That is the living English language.
In this case, there is no difference because you can only start a process that then continues. So the progressive aspect of "working" is redundant, being already provided by "started".