You say "OEM serial number".
Do you mean her 25 character Product Key found on a sticker on her PC, with a format like this:
You can use that Product Key, but it shouldn't contain the characters "OEM" and is not a "serial number".
I think you could use your own disk IF AND ONLY IF it matches the Windows 7 edition mentioned on her product key.
You can definitely download a legit Windows 7 ISO from the following link, burn it to a disc, and use her Product Key. Make sure you download the version matching her Product Key: Official Windows 7 SP1 ISO from Digital River « My Digital Life
I'd make sure I had all Toshiba drivers
for her PC downloaded separately. You never know which you might need. The drivers provided by the Windows 7 installation disc should work for most if not all functions.
I'd particularly want to have the necessary Ethernet/wireless driver
on hand as it may be needed to establish an Internet connection after you clean install.