With all the problems you are having, I'm almost afraid to ask .... but did an owners manual come with your car?
The owners manual for my 00 LS400 shows the location of the two fuse boxes -- a small one under the dash on the far left on the drivers side and the large one in the engine compartment. It also shows the function of each fuse. The inside of each fuse box cover in my 00 LS shows the function of each fuse. I assume your LS430 owners manual contains similar information.
My 00 LS400 has two fuses associated with the radio. The one under the dash is shared by the radio, outside mirrors, shift lock and A/C. I would notice immediately if it blew. The one in the engine compartment is only for the radio. Your LS430 may be different.
The "radio 1" fuse in the engine compartment of a friend's 99 LS400 failed a few months ago. We tried replacing it but the new fuse blew as we inserted it. We disconnected the battery terminal, inserted another new "radio 1" fuse, and reconnected the battery. The fuse didn't blow this time and the radio and CD player again functioned normally. It seemed odd that we had to disconnect the battery to keep from blowing a new fuse.
Has the 90,000 mile service been performed? There should be a sticker on the engine cover showing that the timing belt has been replaced if the 90,000 mile service has been performed. If it hasn't, you'll be spending about $1,500 to have the 90,000 mile service performed.
It is starting to sound like the previous owner let things go. I hope you can verify that the car has had at least a few oil changes along the way.
I don't really think that 90,000 miles service has been done. Owner's manual is missing. I've been told by truck driver that battery was dead when he was picking up the car. Dealer put a new battery in the car...maybe they blew a fuse.