Prospector, Sorry but i have more bad news for you, the Hynix HY27UF081G2M is only a 1GB chip
HERE so that was the start of your problems because the chip was hacked so it appeared as 4GB.
Dump.bin is a firmware backup extracted from another player using s1fwx program. There are 2 reasons why you may be having trouble loading dump files, firstly they may not be repaired in which case you need to make sure they are named dump.bin and put them into the s1fwx folder and run the repair.bat. If you get a failure warning the file has already been repaired. The second reason is that your player needs a Full Version firmware not a dump.
When a dump.bin is extracted from a player not all files are copied some of the files needed for your player to boot and run are not included so if your player is dead a dump.bin will not repair it. You need to use a Full Version firmware which has has the extra 8 files you need, the problem is Full Version firmware are not easy to come by and the chances of you finding the right full version is almost zero.
The good news is you can get around this by installing a Full Version and then overwriting it with a dumped firmware. The difficulty is finding the right combination of full and dump files.
You need to get your player into recovery mode by shorting the memory chip to reset it, the DEAD PLAYER RECOVERY GUIDE will show you how to do this
HERE You will find Full Version and Dumped firmware
HERE
Once you load a full firmware you can keep trying dumpfiles as long as your player is recognised by the upgrade utility, once it stops being recognised you need to short the chip again and then start with a full one again.
If your screen is still blue or black with LCD on after loading a firmware then it was not the right one for your player and you need to keep trying.
I am sorry there is no quick fix for your player, the recovery process can be long and frustrating trying to find the right combination of full and dump files.