It's alright for the chipset heatsink to be hot. As long as your system is not experiencing problems due to overheating, then it is okay.
It is not important to have a Core 2 Duo logo appear in the POST splash screen. As long as the BIOS and Windows recognises the Core 2 Duo E4500 processor correctly, then there's no problem. You can use a program like CPU-Z
to verify this.
For peace of mind, and to just keep up to date, you could
update your BIOS to the latest version (version 0020) if it's not up to date already. It can be downloaded here: http://downloadcenter.intel.com/filt...bmit=Go%21#BIO
. However, if your system identifies your processor properly, and it is working correctly, then it's not advised to perform a BIOS update, since it's somewhat risky.