The reasoning behind my suggestions Nev
I had the same thoughts regarding the contacts on the Ram, the screen is staying black from the outset + the computer gaining an hour to the RTC, neither can be caused by a failed HDD, as post in my reply #4
If this was a HDD/SSD problem it would not stop you from accessing the BIOS, you would get an onscreen message such as what I mentioned earlier ( "no boot device found" ) if it was a BIOS battery problem you would get a checksum error message so this may point to a screen or Ram issue, there are many versions of the Acer One so we need to know the exact one so that we can look for a user manual, this to check out how to remove the Ram and blow out the slots, list of Acer One models here
If an external screen and USB keyboard had been readily available it would have taken only a few seconds to try them both out, it also involves less work and risk than removing the Ram and/or the HDD and that was the reason I suggested the two checks be done first, keep in mind that the Ram is also tested before the HDD as part of the power on self test and when having such issues as a black screen removing the Ram to see if error beeps can be heard is one way of determining if the Ram and memory slots are ok and that it is the graphics solution that is bad, no harm to remove and replace the HDD while the Ram is being removed and replaced though.
Have you tried using battery power only and vice versa removing the battery and using only the AC adapter, if so what was the outcome in both instances please.
Have you reset the time by following the steps that were provided, if yes how has that worked out.
NB: I don't feel that the black screen and RTC setting issue is/are related btw.