Background:
Car has run great since I've had it (just under 1 year).

It occasionally doesn't shut off with the ignition switch, and needs to be shut off using the STOP switch. This started about a month ago and is intermittent.
It also has some vac issues... the door locks, climate control, and one of the windows doesn't work.

It was last refueled about a week ago.

The issue:
It felt weak on the highway driving to work this morning. It was able to get up to speed, however. It had about a third of a tank at the time.

I pulled over and filled it up. This car runs out of fuel when the gauge reads 1/4 of a tank.

It sounded rough and barely responded to the accelerator.

After I filled it up, I continued driving (I was hoping to make it to work).

The problem was worse, and it had even less response to the throttle. The RPMs didn't increase when the throttle was pressed.

I pulled over again and limped it to a station. At this point, it wouldn't even go 20mph on the off-ramp. It didn't want to idle and died.

Now, it cranks but won't start.

My gut tells me that this is a fuel issue, but I would really appreciate some advice on diagnosing this. Since it's an older car, I don't want to risk damaging parts that may not be related to the problem. I tried searching, but I couldn't find this issue on a post already. Any help would be greatly appreciated.

Also, the hand primer is broken.

Get a new hand pump, and work your way along the fuel system front to back replacing the main fuel filter, the pre-filter if dirty, and cleaning out the fuel tank strainer mesh. Also check the fuel tank breather isn't clogged.

You might find the main filter is clogged up and fixes your problem, still a good idea to do the rest if you can though.

Have fun

__________________
1978 300D, 373,000km 617.912, 711.113 5 speed, 7.5mm superpump, HX30W turbo...many, many years in the making....
1977 280> 300D - 500,000km+ (to be sold...)
1984 240TD>300TD 121,000 miles, *gone*
1977 250 parts car
1988 Toyota Corona 2.0D *gone*
1975 FJ45>HJ45
1981 200>240D (to be sold...)
1999 Hyundai Lantra 1.6 *gone*
1980s Lansing Bagnall FOER 5.2 Forklift (the Mk2 engine hoist)
2001 Holden Rodeo 4JB1T 2WD

Running out at 1/4 tank sounds like someone swapped the supply and return lines. How much does it take when you fill it up?
I'd start by replacing the inline fuel filter (the one with the 90 degree bend, looks like it belongs on a lawn mower), and the canister fuel filter.

If your filters are clogging up, especially if someone swapped the fuel lines, it sounds like you have sludge or something in your tank. Hopefully you have a clear inline filter, if it's full of black goo your tank has sludge in it.

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1984 300TD -- summer daily driver
Many others that aren't Mercedes...

Step 1: change the fuel filters. It's always the fuel filters. There's hundreds of threads with people thinking something serious is wrong when its just the fuel filters. I even fell for it once many years ago and posted thinking my tank strainer was clogged... It was just the fuel filters.

If you're one of the unlucky few that doesn't have clogged filters, next is replacing that primer pump. It could be introducing air into the system. A bubblegum fix would be sliding something over it to make it air-tight like a finger glove or small condom.

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1985 500SL Euro w/ AMG bits 130k
1984 300SD Turbodiesel 192k
1980 240D Stick China 188k
2001 CLK55 AMG 101k
2007 S600 Biturbo 149k Overheated Project, IT'S ALIVE!!!

Now that I think of it, I just had an interesting problem recently. I started losing power, but wasn't overheating, oil pressure was fine, so I pressed on to a parking lot and the thing finally died just as I was coasting in. The inline filter had cracked in half around the seam... Could be a problem as stupid as that.
This is why you carry spare filters and the tools to replace them at all times.

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1984 300TD -- summer daily driver
Many others that aren't Mercedes...

Any running issues with a diesel. Unless something else is obvious you change the fuel filters first. Should always have spare filters and the tools to change them in the cars trunk as well.

A clogged filter in the middle of nowhere can land up costing you time and some real money on occasion otherwise.

I forgot to add since you just filled up. Bad fuel can be a remote possibility as well. Small volume diesel fuel sellers can be risky and I try to avoid them.

Your shut off and door lock problems indicate a loss of vacuum. Your power windows may be a fuse; even though a fuse looks good to the eye, it may be bad or only needs to be sanded off for better contact.

Agree with everyone about loss of power - probably fuel filters.