Importance of LOR (Letter of Recommendation)

First of all, thanks for the amazing blog.
I am a Aerospace Engineering Student from INDIA and wanted to pursue MS in Computer Science. My problem is that of getting a letter of recommendation. Professors of CS in my college are not keen on offering courses and projects to other department students and , therefore, I am most likely to be short on LOR. So, I wanted to know that if I score good on GRE and prepare a good Statement of Purpose, how much it will effect my application without a letter of recommendation?