Right..
1) Dnas will only stop you booting your games until you modchip is off or in sleep mode.
2)Version 4 ps2's are quite old and may not even boot backed up games.
3)Sounds like your system is already on the way out and you should sell it on ebay and get a new machine
Try and get v7+
Although v9/10 machines tend to explode due to sonys cheap parts.