Now that you mention it, there is something similar on my Plus. I've never really thought of it as a problem as such, I just assumed it was normal, or if not that it isn’t really an issue anyway. Basically you get a screen that is slightly different to the grey normal background that the Happy Mac appears on (I think it is diagonally-striped, like you say) for a little while (not sure how long exactly), and then the flashing disk symbol (now on the normal background) telling you to insert a boot disk appears.

I wouldn't think there's any way to fix it, if it is a fault - things like this are normally caused by dodgy capacitors on these old Compacts.