I can't offer a complete solution to your issues, but I can educate you on a few things that should help...
First, let's talk about the CMOS battery. Before anything else, let me say this: If you have received the failure warning, you should purchase a new battery and install it. You need a CR2032 or equivalent. They only cost a dollar or two and are widely available (in the US and Canada anyway). Make sure you seat the new battery in the holder properly, with the writing on the battery facing up. If you are not confident in your ability to do this, find someone who is and have them do it for you.
OK, why is this important? For many years, Intel has been working with third-party BIOS developers to move away from the use of the CMOS memory for BIOS configuration storage. The fact is, CMOS memory can be corrupted very easily whereas flash memory is far, far better protected. Despite these efforts, there is still some legacy code - even in the BIOSs for Intel Desktop Boards - that is reliant on the contents of CMOS memory. This is why, for many kinds of problems, the Intel support folks ask you to remove the battery for some period of time. Now, if your battery is not working (or not present or not seated improperly), the CMOS memory will be in a corrupted state. In a perfect world, this just means that you have no current time value but, because this CMOS reliance still exists, this also causes the BIOS to go through a full re-initialization every time it goes through POST (Power-On Self-Test). This is what is causing the boot delay - and could possibly (though I don't know) have something to do with why you have the LAN issue. Bottom line, get the battery replaced and installed properly!
Next, let's talk about the GPU issue. As a motherboard get older and older, it becomes more and more incompatible with new add-in cards - GPU included. These cards are looking for capabilities - things like the PCIe support level, BIOS capabilities like (bug-free) UEFI and even things like the Secure Boot feature for Windows 8+ - to be present in the hardware and either don't work or run in a degraded mode if this is not the case. In the case of the 270, the PCIe support level is definitely an issue, but I also believe that the BIOS driver provided on this card is looking for capabilities from the BIOS that aren't there (or vice versa). Bottom line, if you want the capabilities of a latest-generation GPU, you need (much) newer motherboard and processor.
Finally, some additional comments about the LAN issue. While the battery issue could have an effect, it may also be an issue in the version of the Windows LAN drivers. There are newer versions (with Windows 10 support even!) that can be used with this board. Intel doesn't make them available in your board's download page because they haven't been formally tested with this board and they thus won't warranty them to work, but they should. The LAN driver packages contain support for legacy PHI components, so can support these older boards. While there is some risk of compatibility issues involved (because not formally tested on this board), I would still recommend that you install a newer version. It may have nothing to do with the issue you are having, but it does offer the benefit of fixes for issues in older versions. The latest version you are looking for is v20.2.
Let me know if you have any additional questions...