It has a running problem

I have a 2001 VW Golf TDI and recently it has been acting up. A few times I’ve had trouble starting the car, as if it were cold outside… but it’s not cold outside. Then for the past couple days it kind of chugs along when I’m driving under 45; if normally the engine runs like a rolling tennis ball, a uniform purr regardless of speed, it has been running like a rolling egg. A couple times it has shut off completely at a stop light and I’ve had to restart the car which usually takes a couple tries on my part and up to a minute of trying.
Any suggestions as to what to look for and how difficult it would be to fix myself.
Also, the battery died a couple of weeks ago and this problem seems to have started around that time.

If you recently replaced the battery because it died, did you have the alternator and charging system checked out? On our '01 VW, the alternator died, and there was absolutely zero input in the cabin that there was a problem. No check engine light, nothing. The car just starting acting funny (misfiring), then it (and everything else) just stopped.

If this is strictly a diesel motor issue, I don’t think there are too many here that really work an awful lot on diesel’s. However, there are a bunch of fans here: http://forums.tdiclub.com/. This, I think, may be an eletrical issue.

When the battery died I only had to jump it back to life and saw no need to take it in to have the alternator or charging system checked. No check engine light yet. I think it’s electrical too just don’t know where to start.

You may want to have that system checked out. If there’s a problem with the alternater sending out rippling current (bad diodes or whatever), it can manifest itself in many strange and wonderful ways.

Have the battery & charging system checked as suggested. Many auto parts stores do a basic diagnostic of these for free. (They’re not perfect checks but they are free).

Outside of that you need to provide lots more info. We don’t know how many miles are on it. We don’t know if you’ve ever changed the spark plugs or wires or fuel or air fitlers…etc.

And explain this: A few times I’ve had trouble starting the car, as if it were cold outside… but it’s not cold outside.

You shouldn’t have any more trouble starting the car whether its warm or cold outside. Turn the key and vrooom - whether 90F in the summer of 0F in the winter. So if there’s some history of cold start issues, that might also help to know about.

Your battery died and you didn’t do anything but jump it and now your car is running funny. Did you think it had a self-healing feature?

“When the battery died I only had to jump it back to life and saw no need to take it in to have the alternator or charging system checked. No check engine light yet. I think it’s electrical too just don’t know where to start.”

Yea, it is electrical, like maybe a bad battery or battery connections.

How old is the battery?  I suspect that is the problem.

Many auto part stores will check the battery and charging systems for free.  They  generally do a good job.

The engine has about 250,000 miles on it and is on it’s third owner. I’ve only had it for a year. I’ve never replaced the spark plugs nor the air filter nor the battery. The battery died because I left my lights on all night. The car does turn over a lot more before the engine catches when it’s cold out (below 40F). The only thing I’ve replaced under the hood is the oil. I’ve done a few other mechanical things around the car (brakes, tires, front and rear window regulators, replaced the bumper and side lights) but nothing overly electrical yet.
The previous owner was my brother-in-law and he had the car for four or five years. I’ll check with him when the last time everything was replaced.

Thanks for all the help. I’ll take it in to a auto store and have them run some tests.