It appears to be particularly susceptible to errors when using the cheaper brand of write discs.
I am not saying that Verbatim is, but I would go for a higher quality rewite disc, say SONY or Memorex.
Not to mention those two for any particular reason just that I use them.
I would also try as I said burning at a slower speed.
I appreciate that the disc you last made did play on the other computer, but it may be beneficial just to try the slower speed.
If that does not work then I think we are at the stage of you trying to use that drive in another computer, that it fits, it is used in many HP latops.
Whether that is accomplished by enquiries amongst your friends and acquaintances or through an approach to a computer business is obviously dependant on your circumstances.
At least then you would know beyiond doubt if the drive is good.
Obviously the ideal situation would be another drive tested in this computer.
I will wait for your reply when you have the RW discs and have tried the slower burn.
I do not recommend that you alter any other settings on Img Burn.