I am a caregiver who has lost all motivation to do anything. (I borrowed that line from a previous question that is now closed). Ideas?

My suggestion is to seek professional counseling. Just being able to unload, or even just sitting and crying, with someone who is non-judgemental and can offer reasonable suggestions and emotional support may be very helpful.

Oh, my. You have been through and are going through something horrific and so difficult. I can sort of relate to this feeling you have because my husband died by suicide in front of me and I felt much the same as you do. I could not function, I just did the necessities for a long time and I couldn't even concentrate enough to read the mail. I think you have gone through a similar sort of stress and exhaustion and it is still with you. IMHO, you just need time. Time to grieve, time to recover. This is a difficult time for you to see your father failing after you lost your mother so recently. I don't thing there's anything wrong with just putting one foot in front of the other until things get better. Rest, order out, take a walk. What helped me through the difficult months was talking with friends, getting lost in ridiculous (unemotional--mostly I watched Game of Thrones or Stranger Things) tv to distract from my thoughts and exhaustion and photography. Every day I tried to find beauty and try to take a photo. And then I posted it privately and journaled about it. Some days I took a photo of something and wrote about what you just said above. I also saw a grief and regular therapist and a support group really helped me a lot. Try to talk to someone you trust about all this or come here, of course.

Life is so hard sometimes. Of course you are exhausted and unmotivated. By "take care of yourself," perhaps take it as don't be hard on yourself. Give yourself a treat now and then and just ALLOW yourself your feelings or lack of feelings. Go through it to come out the other side. I think you seem a wonderful caring person to do all of this for your parents. Some day the sun will shine again for you. Until then, keep going. Sending you best wishes and a hug.

Gwen, what do you mean by "retirement home"? I hope it means that he has help available to him.
You are grieving the loss of your mother, but you might also be grieving the loss of your father. Lookup "Ambiguous Loss"; it is real.
I know how you feel about people telling you to take care of yourself. I do envy you though that you get to go home and have a few hours to yourself. I am my husband's caregiver and he can't be left alone, so a walk or a bath sounds like a vacation to me. I'm curious: how old are you? I'm asking because responses to your issue could be different depending on your age and situation.