Very often when you get a slow Windows start up the issue is with device drivers. Bad driver installs, incorrect drivers, conflicting drivers. These bad drivers can also slow down the system once the OS is started.
There are other possible causes, like defective hardware, but the drivers are a good place to start.
The first place to start is Safe Mode. Does the box run faster in Safe Mode? If yes, then you are on the right track with drivers. If no, then you may have an issue with a core component.
The second is to RUN > MSCONFIG and use the Diagnostic Startup option and see if the operations improve.
The video card drivers could be the issue, and changing the card could solve that problem by default. But you want to test the possibility that the card is OK but the drivers are not by completely removing all the video drivers and associated programs, restart, and run on the basic low res driver and test.
Then you can start to isolate individual components and test. To test you want to disconnect, disable, or stop individual devices not needed to have a running system (sound, LAN, etc.) and see if the problem disappears, then add the devices back to see if it reappears. Then you have your problem device. Start by disconnecting any external devices, like printers and drives.
Post back what you find.