So let me get this straight. You're not refunding someone who sent you money which you have received because paypal has an investigation. So you rather than returning the funds to paypal (which you know very well would hold them if there was any reason to) are deciding to keep my money in your account and neither refund nor send BTC because rather than forfeiting the funds to paypal you want the cash?

 If a paypal account is limited you can't send money, or withdraw money period.

So if I got a refund and my account was under limitation than all that would happen is it would be locked in my account and seeing as how its MY money I don't see that as an issue. However you're keeping the money for what reason?

 If you don't intend on sending BTC then this would be ridiculous. If you've received the funds and have them in your holding then theres nothing stopping you.  

 I want nothing more than to get my BTC and be done with this whole thing but at this point a refund is fine, since it would now appear you are holding my money hostage.

 I don't know how to post images here but if someone can show me I can show my ID phone records and paypal cases that say I made the claim and paypal forwarded it to fraud department and they took my claim as an unauthorized usage. If you have any idea when that letter will arrive that will be great. I am the account holder, I've offered three times now to show you my photo ID, my state ID my school ID heck I'll even show you the credit card the purchase came from now you're holding my money hostage till I get a letter in the mail?

 And I'm supposed to be fine with that?