Answer
(Fatwa: 351/L=99/tl=1432)
In the question mentioned above, you will not be sinful because the fault was not on your part. However, you should get up early so that you could offer Fajr salah with jama’ah. As far as the matter of already offered salah is concerned, you are not definitely required to re-offer those salah, because usually the last time of salah is recorded in the calendars one or two minutes ahead. Also, it is unclear the clock was telling exactly right time. However, it would be better if you re-offer the Fajr salah as a precaution since salah becomes invalid if the sun rises while salah.
لأن وقت الفجر كله كامل فوجبت كاملة فتبطل بطرو الطلوع الذى هو وقت فساد . (شامى : 2/33)
Allah (Subhana Wa Ta’ala) knows Best
Darul Ifta,
Darul Uloom Deoband