I have an HP Pro Book G3 440 after many attempts to install the system I managed to install it but when starting it it takes too long to even show the zorin logo while a screen appears with a green "OK" while the screen flashes
the laptop has an I5-6200 with integrated graphics without a video card
Based on similar threads in the Ubuntu forum, I'd guess that (despite the vanilla i5-6200 with integrated graphics setup) the graphics driver is not loading properly during boot but that the problem eventually resolves. Try running "journalctl" in the terminal or look at your boot logs and see what you find. Also based on what I read in the Ubuntu forum, you might want to make sure that your chipset and graphics firmware is up to date.
To use journalctl to get boot logs type "journalctl -b" into the terminal, as follows:
"journalctl -b" will show the boot log for the most recent boot.
"journalctl -b -1" will show the boot log for the next most recent boot.
"journalctl -b -2" will show the boot log for the boot before that boot.
Depending on how you have your terminal set up, error messages and problems will usually show up in yellow or red. See what you find, looking particularly for any yellow or red entries that seem to have something to do with graphics.
If you find anything that looks like a graphics issue, copy those lines from the log and post them in this thread, so that @zabadabadoo or others with more experience than I have can help.
To install the most recent firmware for your computer, go to the HP Laptop Drivers and Downloads page, type in your computer's serial number, and see what shows up. It may be that the HP Pro Book G3 440 is old enough that there will be no recent upgrades. If there are firmware upgrades available, you may have to install Windows in order to download and apply the upgrades.
Looking at analyze-blame, your other offenders are man-db.service and plymouth-wait-service
This Is Important --These services run through the boot process and even after you are able to log in and interact. Plymouth wait service must run during the wait on other services and does not increase boot time
This is one thing about analyze blame that can be misinterpreted. So, as you look at your output, please keep this in mind.
The next offender is network dispatcher so: