my first really stuck fermentation

So I brewed up a 1 gallon batch from Brooklyn brew shop (blonde ale) and it came out with a lower of than I figured. After producing an initial krausen the fermentation stopped dead, I pitched yeast nutrients and a little bit of new yeast. I think my problem is that it wasn't aerated enough originally, being this late I imagine that if I give it a good idea shake that it will taste awful some it will contribute to oxidation, but if it stays where it is, it's going to be awful no matter what... It has been 3 days since the yeast nutrients and yeast with only moved .001 in gravity from 032 to 031.
Any recommendations before I go home and shake the carboy to no end to try to get the thing to start fermenting again?

How old was the yeast originally? It could be that there weren't enough live cells. I doubt lack of initial aeration would cause the problem you are looking at, especially for such a small batch.

What type of yeast are you using, what is the best by date, and what are the temps that it was fermenting at?

What was your OG? What yeast did you use? How long ago did you pitch it? Did you aerate at all?

I actually lost the original yeast packet some how so I used s05. It said that it was good till mid this year. After pitching, I had them fermenting in the basement where the temp did drop the first day to the 50s, so I figured it would just be a slow restart as it warmed up when I brought them upstairs. They have stayed around 70 for the past week and a half.

I did shake to aerate originally, but I fear I may not have shaken it up quite enough...

Was the beer kit an all grain/ partial or extract.

What may be the case was the sugars were extracted from the grain at a temp that caused them to be unfermentable, which would be caused by mashing at to high of a temperature. Which would explain the "stuck" fermentation. Aeration is not really that big of a concern with such a small batch.

It was all grain, if it was a case of mashing to hot, is there any way to fix this? Add dme?

Well the residual sweetness will be there, you could try to dry hop it to cover up the sweetness, but if you are looking to bump the alcohol content I would probably say an infusion of some DME would be the best bet

I would imagine that it would probably also be smart to add the dme in doses over a period of time? Or would it be best just to add till it hits the desired over all gravity?

how much of that packet of s-05 did you pitch?

you could heat it up that might help

You will need to boil the DME with some water to make more wort, then add it into the fermentor. The volume will increase and the FG will decrease. I would suggest just doing it all at once. Its only a 1 gallon batch, and I dont typically leave my beer in the primary for more than 2 weeks. Especially if there are hulls or other things in the trub it can give it an off flavor.