Ideally, you'd locate an old copy of your resume which would have the information on it. Did you ever post a resume online? Perhaps you could search for it.
Failing that, what other records do you have from that time? Do you have any copies of old tax filings? Photos from a farewell party your co-workers might have thrown for you? Go through your old filing cabinets and see what you can find that would help you pin things down.
Are any of your job start or end dates anchored about other life events, like moving, buying a house, or the birth of a child, that you could use to reconstruct dates?
If you really can't find accurate dates, I think it's fine to put "approximately" next to the dates in your resume for those jobs whose dates you cannot pin to a specific month and year.