I have read of such incidents before, some had only need replace the jack of the charging port, if thats exactly what occurred on your laptop. Secondly if its the jack i would also replace the charger also as it could have been damaged. Repair shops will probably have you replace the motherboard completely, granted this may be needed but sometimes only the jack needs replacing which is far, far cheaper than entire motherboard and if its the case of a new board i would rather get another new laptop. I get suspicious if something else goes wrong immediately after repair. Good to check on sites like hello peter if they have been flagged by other customers for shoddy repair jobs.
Try turning the laptop on with only the battery connected, luckily you may boot into windows, which means the jack needs replacing and probably the charger. If you get into bios and get a windows error, try booting from windows cd/dvd.