Looking at the specs for that computer, HP Pavilion p7-1154 Desktop PC Product Specifications HP Pavilion p7-1154 Desktop PC - HP Customer Care (United States - English)
the two DVI ports are DVI-D, which is digital only and won't work with w DVI-VGA adapter. For it to work with the adapter at least one of the DVI ports would have to be DVI-I, which supports both analogue (VGA) and digital (DVI).
Unfortunately what this means is that what you want to do won't work with what you have, and leaves you with basically three choices,
1. A new monitor.
2. A cheap video card that will allow it.
3. Look for a DVI-VGA converter, which is not the same as the adapter that you bought as it converts the digital video signal to analogue; where the adapter just pass the analogue signal through with no conversion.