My concern is whether it's safe to work on my company's computer while at home. I work for a San Francisco start-up. Will they claim ownership over the work I've been doing outside of work just because it's on their computer? It doesn't conflict in business area in the least, but I'd rather go buy a separate computer if there's a serious concern about claims of ownership or potential for getting sued.
Just don't do it, period. And forget the whole idea, please.
Back a few decades ago, when resources were 1000x as expensive as they are now, one might have entertained the thought of using one's work computer for personal and/or side business projects on the sly (and a great many people did, in fact). Resources at any significant scale, or desktop setups for visualization of any kind (even just high-res images -- forget about video!) were basically unobtainable for regular people. Compilers, IDEs, documentation -- that used to all cost serious money (and shelf space).
But these days? Your laptop (which would blow away anything in existence 20 years ago) costs as much as a moderately expensive car repair. And hosting + computational resources are as cheap as water. Languages are so powerful that your main challenge isn't creating stuff -- it's creating in away that's maintainable for your, and understandable to others.
So aside from the ethical aspects of mooching off one's employer, there's just no upside to it. In fact you might want to ask yourself why you're even thinking of this route -- are you, internally, basically expecting to fail? Do you really think you can't bootstrap yourself through this project, like many thousands of others like you (including many far less skilled) -- in this, the very dawn of the age of ubiquitous, nearly zero-cost computing?
Long story short, they did have to make concessions when they were caught but it basically worked out for them (as history has shown).
To echo the previous sentiment; JUST DON'T DO IT.
I haven't gotten an update on how their product is doing now though, but hopefully soon.
If you walked in to work tomorrow and got fired on the spot ("Give me your laptop and leave the building"), would you be comfortable just handing over your machine, then turning around and walking away? If not, that's a problem. It's a problem for you, and a problem for your employer.
Best to keep things as separate as they can be.
If money is an issue, grab a refurb thinkpad, or a chromebook, or something else cheap and work on that. If you even once have to talk to a lawyer for an hour to resolve the issue otherwise, that's already the cheaper option.
If you don't do well and generate revenue/attention, nothing will happen.
If you do do well, then they might come after you with some lawyers, and at that point you have stuff to lose and are wondering why you spent all this time and effort and didn't spend 2k on a laptop of your own.
Is asking your employer about this directly not an option?
Lawyers, IP law, these are dangerous areas and you want to steer clear. In fact if you have written any code on your company computer, delete it and re-write it from scratch once you get your new laptop.
But it still seems like a terrible idea.
I can't believe someone, in this day and age and where you're located, who wants to start up a software business doesn't own their own computer. That's just weird. You're weird.
Seriously though, it's very foolish to be so cheap.
Plus, depending on your state law, they may own stuff you do on your spare time if you don't have a document listing projects that belong to you.
Edit: I'm not a lawyer, rules depend on state law, you should ask one specialized in your state of residence.
Their hardware, their policies. It's certainly not your rules.
Buy a Notebook!
Better use a good encryption, and be sure the metadata doesn't provide them with that proof.
Just use your own cellular, if you need to exchange personnal data from work!