Hi filthywombat,
I have done some research into your product and typically there are no electable power cords for laptops because as your experiencing it is inconvenient when you don't want to rely on the battery. It could be a lose connection as you mentioned that it wiggles.
At this point if you are in warranty give HP Total Care a call at 1-800-474-6836 in North America or visit the link below if you are outside North America.
http://www8.hp.com/us/en/contact-hp/ww-contact-us.html
Thank you,
