Hmm, one thing the D and A have in common is that they both go under the string tree. Have you checked that the tree is firmly screwed in?
If it's not that or a dodgy string then the problem must be to do with the bridge or nut. Try the following one by one to see if you can isolate which:
1. Press the D string down just behind the second fret and while its 'fretted' tap on the string just above the first fret. There should be a slight click or ping as it hits the first fret indicating that there is some slight clearance and that the nut is cut correctly. If there's no click/ping then the nut may have been cut too deep (can be easily fixed with a little super glue) and the open D+A strings may just be grazing the first fret
2. Loosen all strings, place something like an allen key under the strings in front of the nut (put a business card underneath it to protect the fingerboard) so that the strings go over this rather than the nut itself to take the nut out of the equation, bring D+A strings up to tune and check
3. Raise the D+A saddles at the bridge a turn or two to make sure you're getting good string contact over the saddle and check
Then report back!