You need to revisit several aspects of your approach. First and foremost, ratio in cloning are NOT volumetric, but based on DNA molarity. So a 3:1 insert to vector ratio should be 3 moles of insert to 1 mole of vector (not 3 uL to 1 uL or 3 ng to 1ng). For most ligations, use 25ng of vector is more than adequate. The amount of insert is calculated as follows 25ng * (size of insert in bp/size of vector in bp) * molar excess of insert (i.e. 3, in a 3:1 ratio).

Second, while it is theoretically possible to digest and ligate exceeding small amount of DNA, it is not good practice especially for beginners. If at all possible, try your insert digest with 1-2 micrograms of DNA, and similar amounts for vector. Otherwise, when you try to isolate it, you risk losing too much and having low quality and/or excessively dilute DNA.

Heat shock steps generally should not exceed 45sec. If you are making home-made cells, try a few different times to optimize. If commercially produced, follow the manufacturer's suggestions. Excessively long heat shock will kill most of your competent cells.

Lastly, not all enzymes can be killed by heat-inactivation. Please check if you are using heat-inactivatable enzymes.

I could be wrong, but I believe DH5a cells are optimized for a 45 sec heat shock at 42c (rather than 2 minutes). Competent cells are very fragile and the extended heat shock may be too much.

You may also want to try cleaning up the restriction digest reactions before moving on to the ligation step. Competent cells are sensitive to glycerol and it's best to minimize carry-over from multiple reactions. I usually do a phenol/chloroform extraction followed by an ethanol precipitation with 0.3M NaAce, but a PCR clean up kit works just as well. You only need a few ng of plasmid DNA for an efficient transformation, so I wouldn't worry about low yield after clean up.

Finally, acquiring ampicillin resistance doesn't take as long as say, Kanamycin. During the outgrowth phase, immediately after the heat and cold shock, only shake them for an hour at 37c. You are not benefiting from a longer incubation without antibiotics; in fact, the longer the cells grow in a rich media like S.O.C., the more likely they are to dump the plasmid because they would rather not expend the energy maintaining antibiotic resistance they have no use for.

Hope that helps. Good luck with your project!

My two rules for successful cloning are:

1) good quality, and well cut DNA;

2) competent cells with high efficiency.

In your question you don't say if you are cleaning the DNA after the restriction digestion. Do you purify it at all, either from a gel or from the digestion reaction? Also, did you check the efficiency of your competent cells? Once you are sure that the DNA is clean and the competent cells are highly efficient, then you can work on other details of the cloning. Other things worth looking at: ratio of vector to insert; correct choice of restriction enzymes; correct antibiotic; working ligase.

I always cut at least 2 micrograms and then gel purify or PCR purify and elute in 30 microliters. Then I load 2 of that on gel and spec 2 with a Nanodrop to see if they match each other. Then I perform ligation based on what I see. I never calculate for an exact 3:1 ratio. Common sense works perfectly fine.

Important is that I want to see a nice cut band after digestion and purification. Using this strategy results in success close to 100% of my clonings.

Cutting 30-100 ng would not show much DNA on a gel when checking after cutting and purification.

Related to the heat shock, I once titrated the amount of heat shock, using 15 second increments going from 0 to 2 minutes, surprisingly did not result in much difference between the different conditions using my own home-made cells. Even no heat shock resulted in transformation, albeit somewhat less. So I ended up sticking with the 30 seconds I was reading about in most protocols.