STM32 SysTick timer - Doesn't run the alarm event
You have created quite a problem for yourself by ditching the standard peripherals library (SPL). This microcontroller is hard enough to learn with it, let alone without. The library may be horribly designed but it has an advantage of actually working. I suggest you first get a simple test program working using SPL, then gradually reimplement its functionality if you really can't use it (I'm yet to see a technical reason for that however).

In order to use an interrupt in a Cortex-M3/M4, you need the following:


a stack. The core automatically saves several registers on the stack when an interrupt fires. Initial stack pointer value is read from address 0x0 the first thing when the core starts up. That value should normally equal to the end of RAM + 1.
correct vector table offset in the SCB-&gt;VTOR register. By default it's 0, which (again by default) is the start of flash. If your startup code / linker script combination sets up the vector table correctly, great. The SPL does that. You don't seem to (unless it's in the code you didn't post). Look how it's done in the standard peripherals library (startup_stm32f4xx.s and corresponding linker script for a gcc-based toolchain).
a handler. you have that.
address of that handler + 1 needs to be in the correct position in the vector table.  The way you're assigning a value to a location in the (assumed) vector table isn't going to work by default, since it's in flash. It makes me think you have remapped your RAM to start at address 0, but there's nothing in your question that would indicate that.
the interrupt needs to be enabled in the NVIC and its priority set. I don't see that in your code at all. This uses NVIC-&gt;ISER[x] and NVIC-&gt;IPR[x] registers. See implementation of NVIC_Init() in the SPL and PM00214 section 4.3.
finally, the peripheral needs to be configured to generate actual interrupt requests. Seems like you're doing that.


If after checking all that you still can't get it to work, posting a complete (but minimal) project to analyze would be best.