I also have multiple versions of Inventor running on my system as well as other CAD programs. Never had an issue.
One thing to note whenever installing a program, especially on an older computer (laptops are even worse due to travel) is to run an error check on the drive.
If there are file structure errors on the drive it can cause all kinds of fun..
A quick search will give you the steps to run an error check.
You should be doing this as well as defragmentation every so often as standard maintenance.
Also depending on your level of computer knowledge, there could be programs running in the background that can cause issues, that you can try disabling as part of the troubleshooting process. Again a quick web search...
I would also suggest to turn off any anti virus while installing. I have run into issues with various AV programs running when installing programs.. though Inventor wasn't one of them.. But that will depend on the A/V installed.
Hope this helps..