Unable to access my appstore(cannot connect to the App Store)

Remember that this is a volunteer forum, not official Apple Support. I am not here every day nor for more than an hour or so at a time.

Upgrading a macOS depends upon the model Mac, specifications, and year. To get more information about your computer, choose:  (Apple menu) > 'About This Mac' in the upper left corner of any window, then "More Info..." or "System Report". There's more about this in "About System Information [Profiler] on your Mac" - System Information User Guide for Mac - Apple Support

Use the computer information, including the model year, and the links below to determine what is possible with your computer.

Click on this link to read how to get different versions of macOS --> How to download and install macOS - Apple Support

- The article also has links to system requirements for each OS version which you should check against your exact computer model. For any model produced in the last 5 years or so you should use the system requirements links for each OS version instead. This web site also has a reliable presentation of model and OS version compatibility: https://eshop.macsales.com/guides/Mac_OS_X_Compatibility

- With an old computer it may help to have more RAM (memory) than what is noted as "minimum" for any particular system or your computer may run slowly.

- You may find you must use Safari to get links for High Sierra and later using the Mac App Store application to open to a functioning page.

- Sierra, El Capitan, and Yosemite download as a .pkg. Click on this to have a converted version placed in your Applications folder as an "Install OS..." application. Run the installer and follow the directions.

- Upgrades may take some time (up to an hour or more) to install, with restarts and blank screens.

- If you encounter download problems it may help to download while in Safe Mode Use safe mode on your Mac - Apple Support

Before upgrading, back up at least your data in case something goes wrong. See this support document: How to back up your Mac - How to back up your Mac - Official Apple Support

Check if your old apps will still work with with the OS you want to install - https://roaringapps.com/apps This is particularly critical if you are upgrading to Catalina or newer, as older 32 bit apps will no longer work. To check for those, try this 32 bit application scanner application --> https://www.stclairsoft.com/Go64/

I know my 2012 iMac can run High Sierra (maybe even a bit higher) and I would go to that if yours will. It's an old system but still usable in the modern world for another year or so.

Here are a variety of resources helping with connectivity issues:

If you can't connect to the App Store, iTunes Store, or other Apple services, read this support article --> If you can't connect to the App Store, iTunes Store, or other Apple services - Apple Support

- If none of the suggestions work, try the last one: "If you’ve tried all of the above steps and you still can’t connect, contact Apple Support."

Here's a related article about what to do if you can't connect or sign in to iCloud --> If you can't connect or sign in to iCloud - Apple Support

If your iPhone or iPad won’t connect to a Wi-Fi network, or if you have related connectivity issues, read this support article --> If your iPhone or iPad won't connect to a Wi-Fi network - Apple Support

Here's a case where using a VPN prevented sign-in --> AppStore - Apple Community

If none of the resources provide a solution, contact Apple for assistance:

For support, click here --> Choose your country or region - Official Apple Support Select your country, then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.

or:

Contact Apple for support and service --> "See a list of Apple phone numbers around the world."

Click here --> Contact Apple for support and service - Apple Support

I don't know what a "chrome" is. I know chromium the element, and a Chrome browser (which I presume your old Mac cannot run). We need more details in order to be able to address this issue properly. Which model Mac (I presume this is Mac you are asking about)? Which system version?

The App Stores are accessed using an App Store app. If Apple is telling you that your app is too old and no longer supported then frankly you need to update your software to run a version that is supported. If you cannot update because your equipment is too old then you have to buy newer equipment. No, I don't like that either, but that's the way things are.

I'll add that you should be able to upgrade to OS 10.9 at least and probably higher. I know that the App Store works with 10.9 which I was using just a month ago.

You would have to ask Apple about support. That is quite an old system version and it is quite possible that Apple does not even think about it when designing upgrades to the App Store interface. For contacts and other things to try see:

If you can't download or update apps on your Mac - Apple Support