New battery faulty? Oh yes. How does anyone know the source even if it is one that looks as original? I have a couple of Thinkpads and a Dell and replaced all three batteries. The Dell holds charge quite well but doesn't seem to have the longevity of the original. Both of the Thinkpad types just don't last so long or charge so quickly. One test is to weigh the original battery and see if the replacement is the same or heavier - that may indicate how many cells it contains whatever the identification says.
Per the OP, if the battery shows no charge and it is supposed to have been fixed by the computer shop or whatever, take it back. They cannot charge you for something they did that doesn't work.
Finally to the OP, you will find it difficult to find any new laptop with a mechanical hard drive HDD (nor a desktop for that matter!) Everything these days comes with a solid state drive (SSD) but they are faster than a HDD, take much less power, and being solid state won't fail if you drop the machine. Indeed these days you will find many machines had a M2 SSD which looks not unlike a bar of RAM but does the same job as a SSD. Whichever type of SSD is used they are both easily changed for a bigger size, but I would suggest a minimum of 500GB, or 1TB if you can afford it. As modern machines come with a very fast USB 3.0 or 3.1 as standard you can always buy an external SSD for backup.