Just because you don't have all the resources available to you, it doesn't mean that you won't be able to compete in a triathlon. Sure, you'll need to make sure you have a pool available to you at some point of course, but you can bring yourself up to the point that you'll be ready for it and can train much more infrequently at the pool than you may have thought.
The key is to recognize that this is an endurance race. Therefore, you need to be able to boost your strength and endurance over time and throughout the muscles on your body during triathlon training. For the most part, this can actually be done at the gym so that you will be able to swim when you can, but spend the rest of the time taking care of the muscles you'll need.
Regardless of where you do your triathlon training, you're going to want to make sure you have a trainer to help you and guide you, and you'll need to bring your own strong will and determination with you to each session, regardless of whether you're with your trainer at the time or not.
The technique you'll need to use to train using only equipment at the gym will need to be a strategic one, but it will also be very handy as it will mean that you can do everything you need to do in one place. You won't have to worry about snow, heat or a lack of resources until the last minute. You can make sure that you can turn your body into a machine that is ready to take on the race, even if you're starting from a beginner's position.
The first piece of equipment you'll likely need to use will be the rowing machine. The reason is that the motions and muscles can reflect the same ones that are used when you're swimming. While nothing will perfectly replicate what it is to dive into the water and move through it, you can at least prepare your cardiovascular system and muscles for what it will need once you do get into the water.
Floor work will also be important, including motions such as leg lifts and crunches. These are vital for strengthening the core, which is critical to distance training. Your core muscles make sure your cardio – that is, your breathing and heart rate – will be at its very best throughout a long race, while it also helps you to hold good form, which is critical to avoiding injury.
For cardio and endurance, cycling will also play a vital role, as will the treadmill because you'll need to make sure you're ready for the running component of the triathlon, too, not just the water!