I'd say it may depend on your discipline and the culture of the department to which you are applying. I only have one anecdotal experience of a friend (applied to social sciences PhD) who spent 7 years (on and off) in community college, failed multiple classes, and ended his college career with a 3.2 GPA. Absymal GRE scores, two research projects in undergrad. Wrote a really compelling SOP about how his past has influenced his future goals and why he wanted a PhD. He's now in a PhD program after applying the first round.
Sometimes we forget that adcoms are made of real people. My take is that if a school can't see past your early academic history and will hold it against you, it's not a school you'd want to attend. Imagine how they'd treat you as a grad student. Take time to craft the SOP and PS (if the school has one), since this is the only chance to explain your academic trajectory. Of course, don't focus on the negatives without explaining what you've learned from these experiences, and how you might apply them to your future work as a graduate student.
I highly suggest applying for a summer research program at a ranked university to show that you are ready for graduate level work. Work your tail off there, and develop good rapport with the PI. That person's letter may be the difference between your application making it to the last round vs. being tossed out the first round. I say this based on experience--I don't think I'm the strongest applicant, but I did a summer research program, had my PI write me a strong letter, and I've received 4 interviews from top 20 schools so far (waiting on 3 more).