Not sure on the HEQ5 freeze...might be power? Is it in warranty?
Some DC plugs/Jacks of that type are 2.1mm centre pin some 2.5.....so you can fit a 2.5mm centre plug in a 2.1mm jack (not the other way around) but it will have intermittent connection problems that can fail at the most inopportune time.
See if you can wriggle the plug and make the fault re-appear.
Live view is a real issue with DSLRs and focusing on a star. Some people centre on a brighter star, enlarge in by 5X then 10X, and focus it then slew to their desired target.
But IMHO live-view just doesn't cut it for fine astro focusing. You need a bigger screen...aka a laptop and a software program like
BackyardEOS (BYEOS) or
Astro Photography Tool (APT) to do better focusing and intervalometer control (and much more) with the DSLR.
I use APT...just personal pref though BYEOS is good. APT has a free ver although it only costs 12.7 euro.
But trying to use the back of a DSLR screen for live-view focusing in astrophotography....that is not easy and will all end in frustration.