In order to install any software, it is imperative to ensure that the computer in question meets or exceeds the minimum requirements.
Foremost, Microsoft Office Basic/Standard/Home & Student/Professional/Small Business/Professional Plus/Enterprise 2007 require a CD-ROM or DVD drive. Microsoft Office Ultimate 2007 requires a DVD drive.
Microsoft Office Basic/Standard/Home & Student/Professional/Small Business/Professional Plus/Enterprise/Ultimate 2007 requires a system that has at least 500 MHz (since a Pentium III can range in speed from 450 MHz to 1.4GHz, it seems likely that you've met this specification); & at least 256 MB of RAM (your system's 512 MB meets this & is the minimum amount recommended for Outlook Instant Search).
However, you did not make mention of which service pack (1, 2, or 3) that is installed on your version of MS Windows XP (MS Office Basic/Standard/Home & Student/Professional/Small Business/Professional Plus/Enterprise/Ultimate 2007 requires at least SP2); nor did you mention how much free disk space is on your system. MS Office Basic/Standard/Home & Student 2007 requires at least 1.5 GB (MS Office Professional/Small Business/Professional Plus/Enterprise 2007 requires at least 2 GB of free disk space & MS Office Ultimate 2007 requires at least 3 GB of free disk space. Also, MS Office Basic/Standard/Home & Student/Professional/Small Business/Professional Plus/Enterprise 2007 requires an Internet browser comparable to at least Internet Explorer 6 (IE6).
By the way, OneNote Instant Search & OneNote Audio Search require a CPU of at least 2 GHz & at least 1 GB of RAM. 1 GB of RAM is also the minimum requirement for grammar & contextual spelling in Word. Business Contact Manager requires a CPU of at least 1 GHz & at least 512 MB of RAM. Since you did not mention your exact iteration of MS Win XP (Home/Professional/Professional 64-Bit), it is important to note that "Send to OneNote 2007" print driver, Internet Fax, & Groove Folder Synchronization are not available on 64-bit operating systems.
Furthermore, I do not find it reasonable to quote any more specifications such as those for MS Office Accounting products unless found necessary, besides such specs are readily available at http://office.microsoft.com/en-us/products/2007-microsoft-office-release-system-requirements-HA010166865.aspx?CTT=1
It is entirely possible that the cause of installation failure could be a faulty optical disk drive (CD/DVD/etc.) an invalid product key or perhaps an operating system (OS) which the installation deems to not be genuine.