Bad fuel pump/filter?

1991 BMW 525I, 115k Miles, no modifications.

Well let me start off by saying that this car had been sitting for quite a few years, and I just bought it and brought it home. It started with no problem after an oil change, new battery, and fresh gas. But then I went to start it the next morning, and all it did was crank and crank and crank. Well, I didn't know how much gas the guy had put in it before I bought it from him (he put the gas in before I got there, supposedly), and I saw the gas gauge read empty so I went ahead and put about three and a half gallons in, and after a few more tries it finally started, but it ran horribly and had no power at all. Then I turn it off and turn it back on, and then it runs perfectly. So I drove it around the block and let it run for 15 minutes, turned it off, then turned it back on no problem. So I know this has to be a cold starting issue, which makes me think this has to be a clogged fuel filter or a burned out fuel pump. I had planned to give it a full tune up this weekend (it's my project so it's not driven anywhere), but I wanted to get this issue solved before I start putting money into the rest of it.

Here's a video of what it sounds like, same thing happened today, and after 15 or so tries, I got it to start.

http://www.youtube.com/watch?v=YJdtNJhG3S0

I'm not that great with diagnostics so I'm grateful of any help I can get. For now, I'm not gonna start it anymore because I figured there was no sense in burning the living **** out of the starter just to see if I could get it to run.

Thanks in advance.