yes you can conceive, the length has nothing to do with anything. If you know how long your cycles are, for instance if they are 28 days you add 14 days to the date of your LMP and that should be the day you ovulate. if they aren't 28 days then you minus 14 days from the day you should start your next period.
Of course you can conceive if you only have a 4 day period. The best way to find out when your ovulating is to buy some OPK's (Ovulation Predictor Kit), if you don't want to spend a bundle on them they have them at the dollar store, and they work just as well as any other ones. Hope this helps, and best wishes!
The actual length of the period shouldn't have anything to do with conceiving. It's hard to tell when you ovulate because no one knows what your cycles are and because all women ovulate at different times. If you have regular cycles it's easier to tell. If they're irregular, it could happen at any time.
The length and flow of a period have NO bearing on conception. You ovulate approximately 2 weeks before your period. There are many signs to look for in ovulation, including cervical discharge.