Q: What could cause total power fail when batt is brand new? on 2005 Ford Explorer

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Batt icon came on, went next day & checked batt & alternator. Both read bad (Batt giving less than 10.3v). Quick charged batt to full 13v in 30 min. Started right up. Made 1 stop 5 min. later(no utilities were on). Would not restart - no dash lights even. No better w/ jump. Installed new battery, still NO power. Could Ignition relay or its fuse in the engine compartment fusebox be the problem?? If fuse, would that be the 80 amp? Want to fix this, then recheck alternator before installing this new one, if possible.
(1) Answer
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Got the Owners Manual? It will show/tell you where every fuse is and it's function! Check the fuses first though before anything else is done! Good idea for ANY electrical problem is to check every fuse you can find, with a tester. Every vehicle owner should have one!! 15.00 w/free shipping on ebay, cordless circuit tester.
Have Manual. #58 slot is for Ignition listed, but not shown on layout of underhood fuse/junction box. Is this under where the red batt cable connects to the box? And Right, but my test light was dead when I pulled it out, need to get a new one.
Yes i think that is the fuse you need to check. I ALWAYS checkk all of them, with that tester, only takes a few seconds!