Lab power supply to breadboard

You really haven't given us any actual information to help you with other than you don't want an Arduino shield solution. What kind of power supply do you need? How many voltages, and at what current levels? Are you just powering the AVR? Do you need galvanic isolation?

I have successfully used National's LM5071 PoE PD controller in one of my designs. Depending on how you want to hook it up, it'll give you full galvanic isolation and multiple output voltages. My particular setup gives me 3.3V at 2A and a separately-isolated 5V at 1A. I "slave" an LTC3523 off the 3.3V to give me 1.8V and 5V supplies that aren't isolated from the main 3.3V supply.

Many companies offer PoE PD controllers. National, Maxim, Linear Tech, TI... Have you done any poking through their websites to see what's out there so you can narrow down your search?

EDIT now that I have more information from the edited question. :-)

TI's TPS2370 looks like a perfect fit. It's an 8-pin SOIC device that takes care of the 802.3af spec part and you can drive pretty much ANY regulator off of that. So a really simple supply would consist of the TPS2370 and something like the BD9001 (personally I like Linear's LT1676 but I don't think it has a high enough input voltage spec for PoE) from the previous answer. Two 8 pin SOIC devices, a handful of passives and a small inductor would get you what you're after.

The updates in the question have helped clarify some points, although some concerns have not been answered, and the angle of the photos (not from directly above) makes it impossible to rule out connections to incorrect pins on the breadboard. However I can point out 2 problems so far:

• Schematic shows decoupling capacitors, but they don't exist on the photo of the actual hardware.

  Even if some 100nF capacitors were fitted to the breadboard (as mentioned in the updated text, but not shown in the photo), that does not meet the requirements shown in the ST "Getting started with STM32F030xx and STM32F070xx series hardware development" document (see section 5.4).

  This could result in various problems, but is unlikely (in my experience) to cause permanent hardware damage as reported. Even if the cause of the hardware damage is corrected, you might still have problems (perhaps constant or perhaps intermittent) until the decoupling is also improved to meet the requirements.

• No voltage is being supplied to the V_DDA and V_SSA pins (pins 9 & 8 on the LQFP48 package) - confirmed by the schematic and the photo of the breadboard.

  This is critical and these missing connections could cause internal hardware damage to the MCU. The datasheet and "getting started" documents explain more. Here is one example quotation to make the point clear (datasheet page 42):

  All main power (V_DD, V_DDA) and ground (V_SS, V_SSA) pins must always be connected to the external power supply, in the permitted range.

  On all the STM32 MCUs I have worked with, one common factor is that the documentation states you must supply power to V_DDA and V_SSA even if you are not using the ADCs. This is because an "analog block" inside the MCU (powered by V_DDA and V_SSA) also contains the power on reset circuitry which is always used, even if the ADCs are not used!

  Therefore as a minimum, you must connect V_DDA to V_DD and connect V_SSA to V_SS.

I have run out of time to investigate whether there are more problems and some things (e.g. power supply output spikes/ripple) have not been ruled-out. However that missing power supply to V_DDA and V_SSA needs to be at the top of your list of fixes, for your next attempt.

Read the documents that I linked to see the official ST recommendations for a minimal STM32F0 system.

Update: I am concerned about the missing connections to the ST Link/V2 which you mention. Some JTAG adapters require connections to the target's power, for their internal buffer ICs. I don't know about the ST Link/V2, and I don't have time to research it now. If I was in your situation, I would check this point.