Can I be fired because I am bipolar and have vision problems?

First, forget about what you need or your situation: that is not relevant to the issue. The employer has no legal obligation to make sure you can be gainfully employed. I say that not to be unsympathetic, but to keep the discussion focused.
The first issue is whether the accommodation you need--a different way of training--is "reasonable" or not. There is no hard-and-fast rule for what is reasonable: it is reasonable if it is not too expensive or disruptive, and unreasonable if it is. If for you to learn the job will take them much more more time and effort than training other employees, that may well be unreasonable: the extra time will either delay your ability to being work and/or require them to have a "mentor" spend much more time training you than on his/her own job or training other candidates. You not being able to be trained within the standard amount of time, more or less would likely be unreasonable.
The second issue is, even after you are trained, will your conditions make you much slower or error prone (due to not properly being able to see the icons, etc. on the screen) than other workers? If it did, that would likely be unreasonable, BUT you seem to indicate that on your own computer, you will be able to accomodate your conditions by changing magnification. So it appears that the issue is training, not performance once trained; if you can get past training, then it does not appear they could terminate you afterwards, based on what you write.
Is there a way for you to be get trained without delaying your start? If having your own computer with the software on it would do the job, that would, however, appear to be reasonable: there does not seem to be a valid reason why you would have to peer over another's shoulder when they could have  loaded the software on a machine you could use, adjust, etc. for yourself. If having the software on a machine under your control would have enabled your training--would have been a viable way to get you trained in a reasonable time--then their failue to do this may have been unreasonable and if terminated when they did not take reasonable steps to train you, you may have a claim to bring to the EEOC. So the key issue may be, is there some good reason why they could not have put the software on a machine under your control to train you? If there was some good reason (not merely their usual or customary practice,but something routed in, say, computer security) why they could not, then they would not have had to do this and you could be let go if you could not be reasonably trained in time. But if there really is no reason why the could not have done this, and doing it would have solved the problem, that would seem to be unreasonable, and you may well have a claim if terminated.