Best of luck.
What ever is going on, I am confident it is simple.

I got it started the other day using a battery charger that had a " jump start " option. I would guess the battery is bad because it does not have much power even after being charged. The car will run ok once it is warmed up and will fire up throughout the day as long as it doesn't sit to long. We had a odd day of 54 degrees out and it fired up then okay, with out any jump or charge. Back down in the teens now and I am sure it won't start.

update
 

I replaced the battery and it still won't start. When I cycle the glowplugs the volts on the battery drop from 12.96 to 11.80 or so. After the cycle, the relay clicks and the volts go back to 12.96. I can cycle them as 5 times and still no start. It doesn't seem to be cranking as fast as it used to. Any good tests for the starter? Any other suggestions? It is about 20 deg. out and the heater block does not work.
Thanks

Are you trying to start the engine after the relay kicks off or before the relay kicks off? It should be started while the relay is still on so the plugs are glowing when starting.

Have you confirmed fuel and compression and air?

Before the relay clicks off. Changed the fuel filter, when it cranks, it blows a bit of smoke, it just dons't seem to be cranking fast enough. Maybe all the attempts with the old battery have worn down the starter. Could something be stealing the power? Yesterday, when I tried to fire it up, it was cranking faster but I figured there might be a little air in the lines from the filter change. I charged the battery, but just doesn't seem to crank as fast.

Video linked here would quickly reveal if it's turning fast enough.

Did you mean to post a link? If so, I can not see it. Oh, I think you mean for me to post a video. Not an option at the moment.

lots to check...
 

ADJUST THE VALVES!
Ensure that battery cable terminals are CLEAN AND TIGHT.
Ensure the ground contacts are clean and tight.
Same with starter connections.
Possible worn, slow starter.
ALL these things add up.
Synthetic can also help.
After a couple of hours, with the block heater on, you can hear the "sizzle" of the heater in the block.

Good luck!
We have all been where you are, today.
spo:cool:

Yes, I meant for you to post a video. People with experience should be able to tell you in a few seconds if it's turning fast enough.

Thanks. I have yet to find a write up on a valve adjustment. I don't have any repair manuals so I will keep searching.
Thanks again

The first part of the winter my new to me 300D was a bear to start. I had one GP out and a battery that would only crank for 30 seconds. The new gp would allow it to start at 18°F but not at 8°F.

Installed a new 1000/850cca battery and have it smoke at 4°F the coldest that I have had since.

Since then I also ditched the summer oil going to Rotella 5w40.

It is funny starting at that temp. You do the glows as much as you want then start cranking but don't stop cranking till it is started. Sounds really weird, It picks up speed gradually if it were a gas engine you could hear it fire a bit then let off not so with the diesel.

Valve adjustment pictorial

Mercedes Diesel Valve Adjustment Procedure

Your starter may very well be bad thus killing the battery but I would first insure all glow plugs are working and Bosch brand, valve adjustment and the oil isn't thick. Fully charge the battery, glow the system 3 times....and crank if it won't fire.....get the starter replaced....also confirm that the battery cables are solid and not corroded.

Here is also the Diesel Giant GP check.

Mercedes Diesel Glow Plug Repair

Charlie

One more cold weather startup trick I have used--on my Ford 7.3 IDI (never the Mercedes), is to use a hot air gun ( or the wife's hair dryer) and blow hot air into the air intake for a few minutes. This warms the intake, and the warm air itself is easier to ignite than the cold air.

Thanks for all the help. I will report back after following your leads.