Windows 7 Ultimate crashing - ntoskrnl.exe

Your crash dumps are not showing any finite probable cause. In such a situation, it is better to enable Driver Verifier to monitor the drivers.
Driver Verifier - Enable and Disable
Run Driver Verifier for 24 hours or the occurrence of the next crash, whichever is earlier.

   Information

Why Driver Verifier:
It puts a stress on the drivers, ans so it makes the unstable drivers crash. Hopefully the driver that crashes is recorded in the memory dump.

How Can we know that DV is enabled:
It will make the system bit of slow, laggy.

   Warning

Before enabling DV, make it sure that you have earlier System restore points made in your computer. You can check it easily by using CCleaner looking at Tools > System Restore.

If there is no points, make a System Restore Point manually before enabling DV.

   Tip

• If you fail to get on the Desktop because of DV, Boot into Advanced Boot Options > Safe mode. Disable DV there. Now boot normally again, and try following the instruction of enabling DV again.
• If you cannot boot in Safe mode too, do a System Restore to a point you made earlier.

Let us know the results, with the subsequent crash dumps, if any.

It indicates to a HDD error.

Code:

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*                        Bugcheck Analysis                                    *
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Use !analyze -v to get detailed debugging information.

BugCheck 24, {1904fb, fffff8800b08d158, fffff8800b08c9b0, fffff880012b228a}

Probably caused by : memory_corruption

Followup: memory_corruption
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As the laptop is a new one, better you ask the vendor to test the HDD .

You can Do these:.

1. Update your SSD's Firmware
2. Re-seat the sata and power.
   
3. Run chkdsk /f/r, following the option two of the tutorial Disk Check
4. Seatool for dos: SeaTools | Seagate download
   Burn it in a blank cd. boot from the CD, click on "Accept", wait for it to finish detecting the drives, then in the upper left corner select "Basic Tests", then select "Long Test" and let it run.
   (#3 and #4 are for the 1TB HDD only)
5. Post a screenshot of both the HDD and SSD using CrystalDiskInfo - Software - Crystal Dew World.

But it may (step #2; which is an important check) nullify the warranty.

Yes, it takes. You may try SeaTools for Windows | Seagate, too; or the test using Hitachi's own tool from this page .... 7 Free Hard Drive Testing Software Tools.