You must have turned off your phone when the battery died (after it fully discharged). If you are not using your phone for a long time (more than 2, 3 days) it is advised to keep your phone charged to like 50%-60%.
When the battery is fully discharged and if you do not charge it soon, like within some hours, it is possible that your battery may get damaged.
I guess here the problem is that, even though it shows your battery is charging by flashing the logo, the battery is unable to charge itself. Also if your original charger cannot charge the phone, in my opinion, there's no way that your laptop might do the job.
Have you exhausted the battery? Take it into your local Apple store and they will evaluate the situation. If a new battery is needed there is a low cost offer at the moment.
How to fix iPhone 7 Plus flashing apple logo.
