They can be similar in meaning, but the 'can't' version refers to a real situation; for example, your laptop has been being repaired for the three weeks, and you 'can't live without it'. The 'couldn't' version refers to a hypothetical situation: 'My Blackberry has all my friends' phone numbers, my 'todo' list, my email archive, photographs... - I don't know what I'd do if I lost it. I couldn't live without it.'
Of course, 'couldn't' could also (as there, without the negative prefix ) be used to refer to a past instance of inability, as in: 'However hard I tried, I couldn't undo the knot.' But I don't think your question was about that sort of 'couldn't'.