I'm on sinus meds, which has my thinking muddled, but I'll try to make sense...
Do you have access to your folks mail and bank statements? You might want to start there. Look for direct deposits from annuities, premium payments on insurance policies, etc. As you discover each account and company, if the information is not straight-forward, get their 1-800 number and call, explaining that you are their POA and need to find out what sort of account(s) they have and the current balances. They might request a copy of the financial POA docs before they send details.
The banks can be strange. As POA I wanted to add my brother to Mom's SD box so if something happened to me, he could get to her docs. They wouldn't do it. So we went to another bank and got a SD box together, and I transferred all the original docs there. Each time I add an item, I let my brother know. He is named as secondary POA, if something happens to me.
If Dad will do it, he can ask the bank to add you, but he will have to sign... Ask your attny if you want right of survival on their accounts. It can help settle their estate, but it might leave you open to tax penalty.
I was told the VA won't honor a POA without their own forms attached... if that's an issue for you.
Do your folks have a funeral prearrangement contract? If they do, make sure the original copy is somewhere like a SD box. If not, and their finances permit, see about getting this done over the next few months, so you won't have to deal with it later.
BTW, I tell my mother whenever I use her POA to do stuff for her. She listens attentively, but the look on her face tells me she really doesn't care anymore - it's my job and she's glad not to have the responsibility anymore.
One more thing. Keep a copy of the medical POA/living will where you can find it in an emergency. Hospital ERs will accept a copy, especially on a weekend. It's a comfort, too, to be able to read it for "inspiration" if you are called on to make one of those hard choices.
Hope this helps. Keep us posted and let us know how it goes.