FINANCE:
NSE does offer tests in areas such as derivatives and modules. I am planning to take them up in case I dont make a B school this year. Check out the NSE site. Also, I think there is a dedicated thread here for that topic. Look it up.
As for an equities firm. Try IREBNA: But you need to convince them that you would like to work in this field. DO NOT look for a huge compensation package. But good company though.
Another option ofcourse is doing a 1 year finance course in IFMR- Chennai. The college does good work and I know some guys who did the course before heading abroad to do further studies in finance.
MARKETING:
I am a mechanical engineer and I believe the best option one has in automobile firms is working in vendor or the purchase departments. Many companies do recruit freshers for marketing jobs. Although, convincing them that you want to dedicate your life to the company and have no plans of doing an MBA is tough
Otherwise you could consider working in a KPO. Lots of em coming up nowadays.