As star-lover says it does make a difference as far as your ascendant sign, which is just as important as your sun sign it colors the personality of your sun, and your moon sign which represents your emotions all 3 are in my opinion the most important pieces of a chart not to mention the aspects each will make with each other all your other planets and houses. The rest of the planets should be right, especially the outers but it's the aspects they make with your moon, sun and rising sign, and all of your inner planets, which move fairly quicky.
The rule of thumb is if you don't know your time of birth to go with 12 noon. I would start there and see if it at all fits, then maybe read up good on the signs to try and pin point what you *think* your ascendant and moon might be according to your personality and mix it with your sun sign and go from there. It might seem like they could all somewhat fit but one of them fit better than the rest and your moon will fall close to where it was at your time of birth...not perfect but close.
Good luck, hopefully your mother can remember an approximate time, like morning, afternoon, or night and if not, as minderwiz said you can erect a chart for all 3 times and see