It seems from your description that the DC-In connector is either damaged, loose or faulty.
Use a strong light and a magnifying glass to visually inspect the port and check that the pins are not bent and are straight and parallel with each other. Also check that there is no dust or lint caught in the port. Do the same for the charging cord.
If everything seems OK or even if the pins are bent etc., read on:
First is your laptop still covered by the warranty period? If it is consult the documentation that came with the laptop as to what you have to do to make a warranty claim for a repair or replacement. They may dispute the warranty claim if the pins are bent or if the connector is loose claiming user abuse, just a thought on my part, no proof they will.
If it is no longer covered by the warranty, here is a link to the service manual for your laptop.
Scroll to p.48 to see the pre-requisites and procedures necessary to remove the DC-In cable (with connector).
Here is the part number of the connector, 5C10K57005. If you search online using just this number, (do not add Lenovo or connector or anything else to the search term as it will skew the results) you will get suppliers of the part.
Here is a link to just one supplier. It is shown just to give you an idea of the cost. There are others if this one doesn't suit you. Just search for them. (see above re search term).
Hopefully this is of some help.