Very unusual behavior.
From a hardware standpoint, it would not hurt to change the IDE cable.
How big is your power supply?
Since you said a new motherboard, an older 250 Watt power supply may not be big enough.
Next, you might want to setthe drive parameters in BIOS settings rather than using auto-detect.
Is there a drive overlay (or similar) program installed on the drive?
Many times if you set up a drive with the floppy provided by the drive manufacture, you get a utility installed even if you don't want or need it.
I myself have a couple of motherboards that do not like to re-start.
They go into PC health error mode on a re-start.
So, the mother board is a very likely source of your problem. Especially if the problem did not start until you changed motherboards.
1 thing to check there, is to set the CPU buss and multiplier manually.
I have had several different Socket A motherboards that had strange startup problems until I manually set the CPU F.S.B. and multiplier.
How much RAM is installed?
And, what version of Windows are you running?
Windows 9X / Me has a bug where strange issues can crop up if you have more than 511MB of RAM installed.
There is some concern that some motherboards do not fully clear the RAM on a re-boot, and that may be at the root of your problem also.
Check with the motherboard mfg, and see if they have a BIOS update that specifically deals with hard drive detection, or re-start issues.
If this answer does nothelp you, please add more details on the specifics of your system.
The more information we have, the better we can assist you.
Chas