Sorry to hear about all the problems. Yes, that sounds like it could be low testosterone and/or depression.
Low testosterone can make you anxious, moody, depressed and so this can partially explain some of your husband's behavior potentially. The erectile dysfunction that goes along with it coupled with, in some cases, anemia just makes matters even worse.
Now I do have to add a comment though: even in my worst low testosterone days, I wanted to find answers and I wanted answers. That's what is probably most concerning about your story is that your husband is completely unmotivated and I suspect there is more than just low testosterone to blame. As you know from my web site, many experts believe that that depression itself can lead to low testosterone. After all, it raises cortisol which decreases testosterone if it goes high enough.
There are also likely some vicious cycles going on here: being sedentary and eating poorly simply creates a downward slide in his general health and make a bad problem even worse.
But to answer your question: there is saliva testing for testosterone and it is quite reputable. It is for free testosterone but would give you an idea. That said, I'm not sure what the point is in testing him without his knowledge. If someone doesn't want to help himself, then there is nothing that you can really do.
Maybe some of the other guys will have some ideas on how to motivate someone to get some help and testing. That was never really an issue for me...