What rights do I have as far as the home that I lived in with my boyfriend after he passed?

Probably none, but in a creditor claim for half the value property increased in value the last 5 yrs; you will probably have to follow up with a lawsuit in probate court to enforce your claim; must be filed within a year, not after. Get yourself a probate litigation lawyer.

Unfortunately, since you were neither married nor a blood relative you have no standing in probate.

You have no right of inheritance. You may be able to make a claim against the estate [it has to be probated in order for the house title to be changed] for any sums of money you put into the maintenance of the house, but that may be difficult. As you can see, a contract of marriage is much more than the piece of paper many men claim it to be.