All saves are currently stored locally - there are no saves stored on EHG servers - this will only change once the MP features are released… So if you moved machine and didnt copy the local saves then there is nothing that anyone can do - no-one has copies of your files…
If you still have access to the old machine/harddrive, the files would have been in (assuming Windows) C:\Users\USERNAME\AppData\LocalLow\Eleventh Hour Games
Only caveat to this is Steam Cloud Saves… if you used Steam with the Cloud saves enabled, you can try and see if Steam has any old saves in the Remote Store (login via a webbrowser to find them). If steam doesnt have anything or you didnt use it, then there is nothing anyone can do…
As an alternative option, you could get into the old pc if possible, login to steam, and go back into your desktop and use the RUN command and type %appdata%, then click on appdata to the right of your account name in the bar, then click locallow, Eleventh Hour Games, Last Epoch, then insert a flashdrive into one of your USB ports that is compatible with both the old and new computer, and take that Save File and drag it into your D: drive (which should be the flashdrive if I’m not mistaken), then transfer the missing character file from that save folder into the new computers’ save file using that same pathway, ensuring that the character you want to restore is in the date of that file, and also ensuring to rename any “_temp” file association. If there is already a regular file without the _temp at the end, better to transfer that one. If not, then renaming the file without the _temp associated with the character should work before launching into the game, as the game will create another _temp of that one upon launching. Hope that helps as vapourfire helped me resolve my missing character , gold, and stashes today! Good Luck!