I don't think there is a hardware problem severe as it is.
If the machine behaves in safe mode, this suggests corrupt driver/s or major OS bother.
With 98SE, improper shut down always results in a scolding and the scandisk routine.
I am less certain about the bleeps which if they occur, do so early on boot-up. If you know what your BIOS is - Megatrends, AMI and so on you can try Google for error codes and see what is suggested for your BIOS.
About 3 years ago on this forum, scarcely a day went by without someone suggesting the drastic option of Format and a fresh installation.
Obviously that is not to be undertaken lightly and needs all the motherboard drivers as well as a lot of work installing all your applications again.
Dont forget to copy all data to somewhere safe if you choose the format option because it will wipe you disk clean of everything.
It is just possible that you have a virus or some malware which is wrecking the system, but without more idea of your hard disk/s whether you have more than one drive or not, it is difficult to offer more ideas.