IF (and it's always an IF) a new employer will let you work from home full time, logic would dictate that your value to them would be higher because you not only provide your own office space but all the other items you mention - which, presumably, would otherwise cost the employer additional money. But their probable reaction is to say something like "we have established the salary for this job at a certain level, based on the value of the job," and that's the limit of the compensation.

It's not likely they will add something into your base pay to compensate you for all of your resources - and if they do, it might be a very small amount. You might be better off negotiating for a one-time "signing bonus" though it won't be called that. If they were to give you, say, $2500 upon start of employment, you at least have some extra cash in hand and a bit more peace of mind. If the employer is smart, they will realize a signing bonus is better for them also - it allows them to avoid building more money into the base salary, which then gets compounded as salary increases add on each year.

You might also want to think about who will pay the costs of any equipment maintenance or upgrades - it's your equipment but you're using it for their work - you want them to pay, they'll want you to pay - and thus the need to spell it out in advance.