STM32F4 custom board, low voltage on reset pin
One possible explanation for NRST being low, is that it is being driven low by the MCU. That is possible because the STM32 family will drive that external NRST pin, when any of the internal reset modules want to reset the MCU. The obvious candidate in this case, is the power reset, if there is a power-related problem. This diagram is taken from the ST AN4488 application note referenced below:



Since you report that NRST is at 0.4V and not an even lower voltage, it seems unlikely that the reset switch itself is the cause, but it's worth checking that.

On a quick first review of your design, I see 2 main areas of concern:


BOOT1 is floating

Although, with BOOT0 grounded the actual logic level of BOOT1 doesn't affect the boot mode (as shown in table 6 from ST AN4488 referenced below), I haven't seen a design where BOOT1 pin is left floating. While I doubt it would cause the specific symptom you report, I would fix it at a valid logic level. FYI the STM32F4 reference designs have 10k resistors in series with both BOOT pins, before they are then pulled high or low externally, as required.
VCAP1 and VCAP2 are connected

This is my main concern. I haven't seen the internal MCU architecture to show the difference between these two pins (which decouple the internal 1.2V power domain of the MCU core), but notice that in the ST "AN4488: Getting started with STM32F4xxxx MCU hardware development" document, these two pins are each separately connected to a 2.2uF capacitor - and not, as shown in your schematic &amp; PCB, connected together and then jointly connected to two 2.2uF capacitors.

Some of the text about this in the above document is a little ambiguous, but the reference schematic on PDF page 34 is clear about how those pins should be used:



Looking at your PCB layout, it seems that you can just cut the track linking your capacitors C11 and C13 to perform the necessary separation. Also, make sure you are using the specified type of capacitors, if you aren't doing so already.

My hypothesis is that this incorrect connection between the two VCAP pins, might be causing the MCU to keep its internal power reset asserted, which is what you are measuring as the logic low (0.4V) on the NRST pin.




I recommend reading the whole of that document, including section 9.3 titled "MCU does not work properly", which may give you more ideas of areas to investigate.