Because the shape of the leaves, it could be anything. N. sanguinea, ventricsa, the hybrid x 'Ventrata', the hybrid x 'Judith Finn' or alata. We need to see a pitcher.

Hi here is some info I found online for you: "With Nepenthes, some species are easier to root from stem cuttings than others. In general, Highlands are easier to root than Lowlands. The advantage of cutting off the vine is that you can produce several new plants from it, and the mother plant will grow new shoots near the base, making it look bushier. Before attempting a stem cutting, make sure you have some SuperThrive® on hand. It's a solution containing rooting hormones and vitamin B1 Cut off a piece of the vine, starting from the top, and make sure each piece of the vine has 4 or more leaves on it. Make the cut about half way between each leaf. With each stem cutting, trim off the bottommost leaf. Stick the bottom portion of each cutting in a glass of water with a couple drops of SuperThrive®. Keep the cuttings under 40W fluorescent tubes for 16 hours per day. Change the water solution daily if possible. At the bare minimum, change it 3 times weekly. This part is important to maintain adequate oxygen levels. In a month or two, you will see the bottom of the stem split open. Roots will appear soon thereafter. Once the stems have rooted, pot them up in 1 part long-fibered sphagnum moss and 1 part perlite. There are other methods to do stem cuttings, but they are all just as involved as this method. This method is the easiest for beginners because nearly everyone is familiar with rooting an avocado pit in a glass of water. The principle is the same. If you read about stem cuttings in books about houseplants, just make sure you leave out the fertilizer." Hope this helps Sheldon

Copied a link for you that I thought had some really good information and advice: http://www.cpjungle.com/nu101.htm Nepenthes sometimes need really exact conditions to grow well. Good luck.

Neps are equatorial and they are adapted to 11-13 hours of daylength. If yours are receiving light from the sun, only, then the plant will stop pitchering until late spring. /you would need artificial lighting to supplement the sunlight. I would remove all dead plant material.