Out of the box, printer won't feed paper straight, keeps jamming

[Althetrainer]

I don't know if this is the correct board to post this but I don't see a tech support theme in the community.  If this is not the right place to ask a question please kindly direct me to a proper board.

i bought a HP DeskJet 3630 from Costco for my husband two years ago.  He kept it in his closet for all that time and today he finally agreed to unpack it for some printing.  We set everything up according to the manual, the ink cartridges seemed to be fine as the test page printed without problems.  

After the test page, we tried to do some real printing that when the problem began.  The vertical feed tray is having a hard time feeding paper down straight resulting in constant jamming.  We pretty much have to remove 4 - 5 jammed paper in order to get one page printed crooked. This is our first HP printer and so far the experience has been awful.

Any suggestions?  We are at our wit's end.

[Althetrainer]

Just to add more information regarding what we have done so far.  We looked up other posts where others had complained about similar problems, followed HP replies to locate the online manual and did the troubleshooting according to suggestions, so far nothing worked.  Yes, we even bought HP paper for printing.  We have tried fixing it for so long that the black ink cartridge that came with the printer is now almost empty.  Not sure if we should buy more ink because if we're going to toss the printer there is no reason to keep putting money into it. 

Here's a video that shows how the paper gets jammed.  https://www.youtube.com/watch?v=qw0QXwzqR_M&feature=youtu.be