I only feel depressed during the first 4-5 hours of work. the remaining 8 hours I feel motivated and relaxed.
Explore the possibility that this effect may be related to your scheduling, natural sleep preferences, eating habits, etc. Perhaps you really just need to manage the transition from not being at work to being at work.
Some thoughts:
--Try shifting your arrival and departure times.
--Is the transition from depressed to motivated and relaxed concurrent with a meal or other break? Try shifting that around.
--Try taking a few breaks. Specifically, get out of the building and take a walk around the parking lot or something.
--Find ways to get sufficient social interaction. Part of the transition away from college is dealing with the loss of a highly social environment that colleges deliberately foster.
--Look for other tweaks relevant to you and your setting, a little change may go a long way
--You're actually enjoying about 2/3 of your time at work--that's a pretty solid foundation for getting to 80% (you do know Pareto's law, right?)
--Many organizational cultures expect and reward presence as opposed to actual productivity. Build some of your non-work activities into your work time in order to gain some of your private time back. You know that old guy who strolls to the men's room with the newspaper under his arm so he can be paid to poop? Sometimes that's just a compensatory strategy to accommodate for a culture that demands time over productivity.
I'm also going to be a little politically incorrect here, but try just sucking it up for a while. Yeah, life is hard at times but getting through tough transitions is a key life skill that you will need many times. Take this opportunity to hone your transition skills. It's not called "the real world" for nothing, and transitioning from the the joyous, care-free life and schedule of undergraduate education to the real world is probably your first big transition and first real test. Frankly, you are also transitioning from child to grown up, from learner to producer, from receiver to contributor. Of course it's hard. Life gets harder at an accelerating rate. To be trite: think of this not so much as a problem but as an opportunity.
I say tough it out for a full calendar year or a bit more. One of the things you'll sell to future employers is the ability to stick it out through projects over time, to be reliable, to show that people can count on you. You need to do this now. A typical college semester is about 4 months with a generous break before the next semester; real life isn't like that.
If nothing else you'll learn that start-ups aren't for you and look for other things later on.