For the most part a digital cable is an all or nothing affair. No "graceful" degradation or anything.
A lot of larger screens, and it is not entirely absent in small ones either, split the screen into sections and thirds is a popular choice. All sorts of things can happen to the driver segments and cause whole vertical sections to go funny (that you said blur as well, had it just been darker then it could be a segmented backlight). I am surprised that switching dp to hdmi helped for a while, had it been a decoder issue then maybe but this does not sound like that. Unless you drove it at a lower res/frequency on HDMI I guess, or maybe the simple act of manhandling it sorted a loose connection.
Anyway various options from the ribbons coming away from the driver PCB or where they join the LCD (rather than connectors and the fun that comes with that they often do something called hot bar soldering which is much as it sounds and not amazingly reliable). Sometimes said ribbons have a chip on the ribbon that could be failing and if it was a heat/loose connection affair then that could say why unplugging it for a bit sorted it. If there are connectors then remove and replug.
Otherwise this is something someone that has some gear can fix, it is not like replacing a few capacitors on older monitors though where you can do it trivially and barring the replug thing this will probably not be a simple buy a replacement board from somewhere and install it affair either. If there are any TV repair places around you then they will hopefully be able to do it.
Skip to about 3:30 in
All those ribbons going off down the bottom are what I am talking about.
Hope you have a warranty. If it is a UK buy then read up on the sale of goods act (entitles you to several years) and if you got it on a credit card and paid more than £70 or so (check wording in your contract) then the credit card company will often warrant things, though it is mostly for when the original shop has gone out of business.
