Too big to enter the gel.

Exactly, try preparing gel with agarose concentration below 1-0,5% or even lower. Keep in mind that gel will become very fragile and will melt easily. It may be necessary keep it in refrigerator.

Try some lower concentration gel and again purify your DNA. It seems there are some impurity of Protein in the sample. Proteins are larger molecules in comparison to DNA and they tend to stick in the well of gel.

116kbp is indeed very large for a circular DNA to migrate into an agarose gel. When I was a postgrad student I had a brush with pulse field electrophoresis, and surprisingly I did learn at that time that with this vechnique open circle DNA would migrate much less than larger linear DNA. the "simple" idea is that large open circles will "impale" themselves on the agarose chains that make the gel sieve.

And I would guess that even after linearisation your 116kp fragment would not migrate that much inside the gel.

I also did run a couple of times 0.4% agarose. You can't handle such low concentration gel, so basically everything was made inside the mould (and even some people were first pouring a 1% gel and then the 0.4% on top of this one in case you need to handle it). Even so, it's a pain to work with. You can also rather use low melting point agarose.

I am agree with M. Ashfaque, it might be some protein there so you should incubate the DNA at 37 degree centigrade for 45 min with Proteinase-K (final conc. 100 micro gram/ ml) and use 0.7% agarose gel.

How did you solve this problem? I am facing the same issue. I am cloing the cDNA but the band cannot migrate