Yeah, uberman is right, you cannot boot your new machine from this drive - the drive does not have the device drivers needed for your newer machine.
However, you made a common mistake. Just because the HP's old drive is being installed in (your) machine that already has its boot drive established does NOT mean the HP should be jumpered as a Slave. Setting Master or Slave with jumpers is ONLY a means of uniquely identifying the two devices allowed on a standard IDE port - it has NOTHING to do with how many other drives are somewhere else in the system.
IF you have an IDE (aka PATA) port in your machine AND you have an 80-conductor ribbon cable, your easiest route is to simply connect the old drive to that port directly. Of course, you'd also need to connect a 4-pin Molex power supply to it. If this is the only device on that port, set the drive's jumpers to Master (or Master with No Slave, if that's a special setting). If you already have an IDE device on the mobo port and cable, and that existing device is set as the Master of the port, then set the old drive to be a Slave and connect it to the middle connector of the ribbon cable. On the other hand, if you have an IDE device with its jumpers set to "CS" or Cable Select, and connected to the END connector on the cable, then set your old drive to "CS" also and plug it into the middle connector.
In some cases with new machines the IDE ribbon cable supplied has only one connector on the end. You can always replace that with a cable with an added middle connector - ALL IDE ports can handle 2 devices.
If you go the route of connecting to a mobo IDE port, you should check in the BIOS setup screens to ensure that port is Enabled and the BIOS can see the drive there.
Now, if you want to continue using the adapter to convert this IDE device to a SATA device, read the adapter cable's instructions carefully. It may require that the old drive be set to Master, because a traditional IDE port MUST have a Master and may have an added Slave, but can NOT work with only a Slave.
Similarly, if you opt to buy an external drive case that can accept an IDE (aka PATA) device and mount the old drive in there, read the case instructions carefully. I expect you must set the drive's jumper to Master.