Mobo to replace my old desktop!

This is a Dell forum and I suspect you would get more information on the ASUS site from their forum. Secondly that is extremely old hardware and any compatible MB would usually only be found on EBay for instance. It might be time to consider a new, faster, up to date system.

The case is doesn't matter for me because it's also a junk!

Your late ASUS board is microATX LGA775 socket Intel 945 chipset.  In Dell optiplex there is almost no equivalent microATX board for LGA775 as almost all old optiplex core2duo pc are BTX and would not fit your case. However, Dell has microATX LGA 775 in the Inspiron and Vostro series that may work for you. 
JOCean is correct that invest in an old Dell board to replace your ASUS board may not be worth it.  But just for theoretical planning discussion, you can get an Inspiron 530 or Vostro 200 motherboard, both will accept your core 2 duo cpu and ddr2 ram.

your ASUS IO shield would not fit Dell board. ASUS front panel power switch uses different pinout from Intel industry standard 9 pin used in Dell 530/200.

ASUS 

Inspiron 530/Vostro 200

@redxps630 

If you want to upgrade the case it is better to get a microATX or ATX case. BTX case are not future proof. 

This is also nonsense.

Micro ATX and BTX are mirror images of each other.

Intel DG965MQ, D37419-302 LGA 775/Socket T  Micro BTX  is a similar Micro BTX Design as the GX620.  Dell worked closely with INTEL on ATX and BTX as well as Micro ATX and BTX.

https://www.ebay.com/itm/304002060503

Buzz words are not specifications and should not be recommendations.

@DELL 15R N5110   GX620 tower would be a GOOD option for a DELL.  If you plan on adding more than 4 gigs of Ram I would recommend XPS400 instead so that you can get the full 8 gigs of ram and use your GPU. This too is based on the LGA 775 Socket T and works with ALL os just like the GX620. Buying a system like this gives you an upgraded power supply as well as other parts that can be re used from your current system.  The benfit of either is that its a Dell and is fully documented, upgradeable and maintainable well past 2025.

https://www.ebay.com/itm/254283607211

But the problem is that in our country there are no any give away people! They are trying to stole our PC hardware in work shops also!

@DELL 15R N5110 

You can migrate ALL of your parts to an OPTIPLEX GX620 Tower without issue.

@redxps630 

"Your late ASUS board is microATX LGA775 socket Intel 945 chipset. In Dell optiplex there is almost no equivalent microATX board for LGA775"

That is complete nonsense and false.

The optiplex GX620 tower is LGA775 and uses Intel 945 graphics is micro BTX which is the same as micro ATX except Mirrored and RUNS all software from MSDOS to windows 10 when equipped with an LGA775 pentium D915 or greater cpu.

Which is also not expensive

https://www.ebay.com/itm/224543745038

These are not expensive systems and they are fully useable to 2025 and beyond.

BIOS should be updated to A15 before changing CPU if it doesnt have a pressler pentium D900 series.

https://dl.dell.com/bios/A11GX620.EXE

All of the items in the 2007 FAQ still apply

https://www.dell.com/community/Desktops-General-Read-Only/DELL-OptiPlex-GX620-FAQ-Frequently-Asked-and-answered-Questions/td-p/2528727

Tower models are recommended due to power supply size on the smaller units.

https://www.ebay.com/itm/264829248768

I think that Optiplex GX620 is a good computer. But I wanna know can I run it on windows 7 without issue? (Like drivers and BIOS updates)

@DELL 15R N5110 

Once you update GX620 Bios TO A11 and Install pentium D915 processor it will run ALL os from MSDOS to Windows 10.  Not supported does not mean not working. MAX RAM on a GX620 is 4 GIGS with 3.5 useable. DOES NOT MATTER IF OS IS 32 bit or 64 bit.  Onboard video steals 512 megs and you never get that back.

Windows 7 / 8 / 10 need the ram Maxed out or it will be horribly slow.

The GX620 is special in that way that it runs all os all versions.

Its not particularly fast but its not slow when the ram is maxed out.

915 cpu is not expensive at all.

Bios should be updated BEFORE changing CPU if you do not have A11 with a pentium D installed.

https://www.ebay.com/itm/114834178025

There are no drivers for windows 7 / 8 /10 for this model but the WDDM 1.0 vista drivers work fine.

The audio and chipset and video are not native to windows so those are the drivers you need.

This is an XP system that is VISTA capable.

Been there done that.  I would recommend windows 10 over 7 or 8 due to the older os versions being end of life end of support.

Not supported does not mean not working.

Windows 10 as well as Ubuntu 20.04.2 run just fine on this model without issue.