Recovering photos from a broken iphone 5c?

It needs a new battery. Apple is kind of tricky because they don’t guarantee that won’t wipe or completely replace a device brought in for service. But if they did just install a battery you should be fine, as long as you provide the correct passcode. If not they might just wipe it and tell the customer that it’s their responsibility to back it up.

If the data is the primary thing then you might see if a third party repair shop can help. There are a variety of things they might do, starting from installing a battery. Of course Apple may refuse any future service.

If you have all your photos and contacts on your PC, then you should be able to transfer them to your new iPhone 11 without the need for the 5C

The question is: did you transfer all of your 5C photos to your PC? If not, then you may need to put the 5C on charge. It could take some time before you actually see any reaction to being on charge. When you see any reaction to charging, plug the phone into your PC. It will carry on charging while it's plugged into your PC.

When it reaches a certain charge level, your PC should recognise it. If not, take it to an accredited Apple dealer who may be able to help you.

sapper wrote:

If you have all your photos and contacts on your PC, then you should be able to transfer them to your new iPhone 11 without the need for the 5C

The question is: did you transfer all of your 5C photos to your PC? If not, then you may need to put the 5C on charge. It could take some time before you actually see any reaction to being on charge. When you see any reaction to charging, plug the phone into your PC. It will carry on charging while it's plugged into your PC.

When it reaches a certain charge level, your PC should recognise it. If not, take it to an accredited Apple dealer who may be able to help you.

If the battery is truly dead, there no time that would do it. I've got a device that will show the little battery indicator if plugged in, but it never powers on because the battery is completely gone.

I noted that the problem with Apple is that they disavow any data. Every time I've brought in a device for service I've needed to agree to terms that allow for them to wipe the data or perhaps replace the entire device. That is the one thing that I would worry about with the OP's case. Usually they don't, but if the sole purpose is to extract the data that one big problem.