HDD are not turned off after installing graphic card

Hello and welcome hutorny now this is almost identical to my Ivy Bridge setup and I have no real issues with it when installing new hardware.

Now just where did you get the driver for the new graphics card? Is it the same as this one from Nvidia? Drivers | GeForce

Have you got an AV installed? if so it might be an idea to disable it when installing the GPU driver.

I did say I had no issues with my machine except for one an it involved the Samsung Magician software and the issue was solved by uninstalling it so do that if you are running it.

As that new card is a fair size just what are you using for a PSU? it could possibly be under powered.

Edit: I should have also added that it might be an idea too to only have the OS drive installed while you do the driver.

Ok mate well see the suggestions that johnhoh has posted first and in reality you really need to update the GPU from the manufacturers site because a lot of software disks that come with cards and motherboards for example are more often than not out of date by the time you buy them. That's why I posted that link for that very purpose.

Now unless I am terribly mistaken that GPU does not need the power supply cable to it and the specs refer to it requiring 75W and a PSU of 300W is recommended by the MSI site.

So what you can do is two things first you can find the specs on the PSU using this
Using HW Info
PART A:
You can test the volts on the PSU with HW Info HWiNFO, HWiNFO32/64 - Download < download the right bit version and close the right hand window select Sensors and scroll down to the power section where you will see what the volts are doing see my pic. In my pic the section (Nuvoton) with VBATT as a dead give away you are in the section for the rail voltages. There are other section titles and one that pops up often is ITE (sometimes the usual one for Gigabyte boards)
Now the voltage on the different rails have to be within 5% =+/- of what is required or the machine will not work properly if at all.
Limits +/- (minimum - correct - maximum)
12v1 = 11.4 - 12 - 12.6v
12v2 = 11.4 - 12- 12.6v
5v = 4.75 – 5 - 5.25v
3.3v = 3.135 – 3 – 3.465v
-12v = -10.80 - -12 - -13.20v
+5VSB = 4.75 – 5 - 5.25v
The Power good signal voltage at pin 8 on the 24 pin plug (grey cable) should be the same as the 5v rail reading/s
See this for the rail voltage info
PSUs 101: A Detailed Look Into Power Supplies (Section 2.)
The original right hand window shows the machine running and is handy for that but for looking at the components in some detail close it and use the main left hand side panel
FOR OTHER COMPONENTS
PART B:
Open each small square with + in it on the section the components are in and then click on the individual component/s (it will highlight in blue) - in the right hand side will appear all sorts of details including brands speeds and other essential info that particular device. See pic for example.

Use PART A: - see mu pic for what you are looking for.

Second you can find out roughly what size PSU you need with what you have in the machine using this
OuterVision Power Supply Calculator < this will give you a suggested output wattage for the PSU and allow for some leeway just fill in the specs as best you can

Ok now the PU has enough obviously though I am not familiar with the brand and quality of build is all important with that device because if it does not provide the power in a stable and adequate manner then it follows that other components will be affected also.

For example a small difference in the CPU operating voltage (say 0.1v) alters the clock speed accordingly so any fluctuations in that will affect the performance of it. Now the main voltage rails are ok that is the 3.3v, 5v and +12v rails. The vcore readings I think if you were to watch them will fluctuate with use. So for the moment the main voltage rails are the ones that should be within that 5% +/- of the required standard voltage as per that ditty of mine.

The next thing is to see if that GPU update has any effect on how the machine behaves.

Intel Smart Connect has to do with waking the computer from sleep. Here is the driver if you do not have it
Download Intel(R) Smart Connect Technology

If after applying it you still cannot wake from sleep, try uninstalling that video capture card just to see if it makes a difference. You mentioned it did not used to affect sleep, but maybe now there is a conflict. Something to check. If you want to post the specific model of the video capture card, that might be useful