2001 325CI poorly maintained.. need advice

So i just picked up this 325CI off ebay.. thought it was a steal for the price.. clean carfax.. 3 month warrenty.. sport package..not a ding or a scratch on the thing.. perfect. So i get it a few days ago, and just got it inspected by my mechanic who i trust with my life and he said it probably had 2-3 oil changes in the 55 thousand miles it has on it. There was burnt oil all over the oil cap and a little inside. That plus the anti-freeze was empty.. and the engine light wasnt on which was an added bonus. The 3 days b4 this ive been driving it and wow.. it drives nice. The first thing i did was get an oil change. But now i must decide.. what to do. Sell it? or keep it and if it goes get a new engine. Plus i tend to push my cars sometimes to the limit and with this i obviously cant due to past maintenance issues. How well are the BMW engines made? Can they withstand this kind of poor treatment?

- very few oil changes in 55 thousand miles
- received car and anti-freeze was practically empty
- burnt oil on oil cap and inside engine
- oil light goes on for a good 15-20 seconds when the car starts then goes off once it heats up.

i feel like crying.. for all the trouble i went through to get this car.

so my question is.. what would you do in this situation?

I have bought cars like this before, although not a BMW. I would wonder if the previous owner used synthetic oils, as that would be a good thing as they can last 15K miles. I have seen arguments that regular oils can go that long also as they are much better than oils of old and BMW's call for a longer change period anyway(my son has a 96 318i). I would not do this, but these engines are engineered a bit better. I would get an "early" change (say 1K) or have the motor flushed to get out any crud and then put the car on a regular service set up, either regular at 3-4K or synthetic at 5K, but of course others may differ on this. If the engine sounds good, runs good, and has no other troubles I would run with it, but not sure about the oil light. See if your friend can do a oil pressure test. If it is OK you should be too, but I would consider getting rid of it if too low. Sorry not more help on this, hard to know what to do in these cases.
I got an old Olds with a beat up 2.5 (90K)on it years ago, really abused. Took care of it and now my dad now drives it with 175K on it. Still going....

I was looking at one that had thick sludge under the oil cap. I spoke with a local oil change shop and they suggested several quick oil changes and running synthetic oils as they seem to have strong cleaning agents.
I have heard some people say motor flushing could do more damage than help.
The oil light really bothers me. Might be worth a new oil pump... anyway:
I also spoke with the local bmw dealer and they suggested having the oil pump checked out. It almost sounded as if their might be a problem with the oil pump and might of been covered under a bmw recall or something like that. The car sold before I made up my mind, so I have no further info.....
Best of Luck.

This is a synthetic car. The scheduled oil changes are every 15,000 miles. So 3 changes in 50k is normal.Do not flush the engine. Just do some accelerated oil changes.

do a little research on those engines(2.5 inline)......i`ve heard that they are they best 3 series have ever had....