I'm new to Islam; I reverted only 3 weeks ago. I'm very excited about Ramadan, but today I accidentally woke up late. Someone told me that I can't fast if I haven't eaten or prayed fajr at the right time. Should I fast or not?
First of all we are happy to hear that Allaah has guided you to Islam, and we ask Allaah to help you to do that which He loves and which pleases Him.
Secondly, if a Muslim sleeps and misses a prayer, and does not wake up until after the time for that prayer is over, then he should not ignore it, rather he should offer the prayer whenever he wakes up. And there is no sin on him for that, because the Prophet (peace and blessings of Allaah be upon him) said: “Whoever forgets a prayer or sleeps and misses it, let him offer it as soon as he remembers, for there is no expiation apart from that.” Narrated by al-Bukhaari, 597; Muslim, 684.
In response to your question:
What was said to you is not correct; you have to complete your fast on that day.
If a Muslim does not eat suhoor or does not wake up for Fajr, this is not counted as a reason for him not to fast.
So you have to continue your fast. If you broke your fast, thinking that you did not have to fast, when Ramadaan is over you have to fast another day to make up for it.