Use a digital multimeter and measure the 12 and 5 voltage lines of the molex connector that connects to the hard drive. If the voltage is high or very low, then you need to replace the power supply. You could have connected the IDE cable backwards. It is a little strange for IDE because it is fool proof but not for 1996 computers and to present. A standard IDE cable contains three connectors. The first connector is about 18 inches or more from middle connector. This connector goes to the motherboard and it is usually a blue color. The other two is either master or slave and these are seperated by about 6 to 8 inches from each. To use cable select, you to have a drive set as master or disconnect a certain wire in the ribbon goes to the last connector.
I do not think it is the cable but a bad power supply because the beep is probably from the hard drive starting up and turning off. I have a PATA Seagate drive and it did this when I figure out that the external power supply was producing 13 volts instead of 12 volts. I bought a Mean Well model D-60A from Jameco Electronics and it works very well.
If you do not want to get a new power supply, you could buy a 5.25 extended cable, schottky diode and a few farad capacitors. Cut the yellow wire (12 volts) and any black wire (negative or ground for either 5 volt or 12 volt). Then strip them. Next place the cathode of the diode to the wire that comes from the power supply and place the athode of the diode to the other end of the extended cable. Depending what WVDC farad capacitors you got. Lets say you got 5 volt versions. You have to get six, nine, or twelve of them to bring their WVDC above 12 volts and to keep the capacitence high enough so the hard drive can turn on. Connect three capacitors in series and then connect them to the athode of the diode. Note the polarity of the capacitors. If the hard drive does not turn on, connect the other three capacitors in parallel of the three that are connected. I think a farad is all you need to kick start the hard drive.
Hard drives that were partitioned and formatted on latest contollers will not work on old controllers because the difference in hardware and software between the two controllers. Some people will disagree, but this problem is true. Hard drive manufactures recommends that you format the hard drive any time you transport your hard drives from one machine and to the next machine.