1. Make sure you are using official Apple chargers. There is a huge counterfeiting problem.
https://www.forbes.com/sites/amitcho.../#26bd85f25b07
2. Make sure it's an official MFi (Made for iDevice) cable in good condition. No surprise here, but good cables are seldom cheap.
3. As for your laptop not charging, how old is the laptop? Older models are short on power. (I had to use a Y-connector for an old CD-ROM drive on an old laptop; it fine with a single connector on a newer laptop.)
4. There is a chance something is wrong with the port on the phone. Make sure that it's clean. Dust can cause problems.
If possible, as in there is a **known-good** phone, cable, and charger to try, that will let you isolate the problem. (Note: New is presumed good, but unknown until tested.)