I started an online software company a few years ago. If I find and take a full time job with a new company while still running my software business is it unethical for the new employer to ask to use my software in their products for free? Or for that matter even if they pay for it?
If you are not giving away your software for free to everyone, you can politely tell your employer that you can't let them have it for free. However, if they want to buy your software, there is nothing unethical about them using it.
Of course, if they have any problems using your software then you will definitely be the first one they contact. As long as you are ok with that, though, there's nothing wrong with that kind of situation.
Keep in mind, though, that if you're going to work full-time for a new company, they could ask that you leave your current software business as a condition of your new employment. Also, if both businesses would be competing against one another, it would be unethical for you to stay with your current company as it would create a conflict of interest.
Your employer probably has an 'anti-corruption' department/contact (usually part of legal/procurement) that should be involved in this. You should contact them, regardless of the pricing discussion. These divisions will make sure that your product is evaluated just as fairly as any other product and that competition is not bypassed and no trade laws are violated.
Usually this will also settle the pricing question, your company should be treated as a regular supplier and thus should make an offer like any other company. Even if this step is completely ignored by your employer, for you this is still the best option. Treat them like you'd treat any other client, not only for initial pricing but also for your SLA (you don't want 'official' bug reports during your lunch break). If you do not think such an arrangement is possible, I'd suggest to back off.