The few startups solving the same problems that actually win against big players (by winning understand biting a fair portion of the total pie to survive) are doing so by solving this problem fundamentally differently. Your innovative approach must be really innovative to stand a chance against the big guys. This has to be something completely different to stand a chance.
Offering lower price will not be sustainable for you in the long run I think. This will definitely hold you back on the growth side. Not to mention what the customer might think - lower price = lower quality. Besides a big player has a lot of resources! They can squeeze you out of the market easily with your lower price.
I am an unsuccessful former founder :) . But I made some similar mistakes. In my opinion, rocket-marketing and completely innovative product are the two musts for the successful groundwork of any startup.