Are you sure the old PC is dead? Replacing one dead component\reformatting\cleaning it out to ensure it’s not overheating and throttling itself could be significantly cheaper than a whole new machine, if the old one was capable of running what you needed to before it died.
Are you looking to buy individual parts and DIY, or looking for a pre-built system?
Are there any components from your old system you can salvage (presuming you’re scrapping it?) Even just the case + PSU could save you a couple of hundred instead of buying new.
What kind of games? The newest AAA FPS Cyberpunk-ish games have vastly different requirements compared to older\browser games, which will affect what kind of hardware you’re after.
Is the “multimedia” work limited to Zoom\MSTeams work, or do you also mean video editing?
Office work like Word and Powerpoint (and browsing the internet, watching youtube\netflix, sending emails etc) can be done on pretty much anything built in the last decade.
What about peripherals? Keyboard? Mouse? Speakers? Headset? Webcam? Do you have\will you need? It would be easy to spend the whole budget on just these things. I’d recommend a mechanical keyboard for typing\gaming (unless you use a controller,) provided you can put up with the noise they make. IMO makes a world of difference, but they can be pricey. If you’re looking to save money, a $20 kb+mouse combo will be enough to get you by, or you can re-use your old ones.
Re the monitor; depending on what type of games you play, a new monitor with a high refresh rate could make games more playable\enjoyable, and use the old one as a second monitor. The teachers I know much prefer working with 2 monitors for WFH stuff. One for the video-conferencing software, the other with their notes\browser\emails etc.
Storage is relatively easy and cheap, (a fast NVME drive for operating system + programs + whatever your “current” game is + a separate SSD\HDD for less frequently accessed\archive stuff.) You might be abe to salvage the old drive from your dead machine and use it.
Unfortunately now is not an ideal time to buy for all sorts of reasons; covid is affecting manufacturing and shipping in Asia, which affects supply here, which affects pricing. If budget is an issue, IMO it’s probably better to get the barebones\lowish spec of what you need now, then once things stabalize you can upgrade certain components\add memory\better peripherals etc if you need to.
Centrecom does have some decent pre-built machines around the $1500 mark (if you are wanting to play AAA games, these can probably do so comfortably on medium settings at 1080. If you are playing older games, you could get away with something cheaper.) Some have better CPUs and not quite as good graphics cards, others are the other way around. Which one is best for you will depend on which games you’re actually playing. The issue is they’re box only: no monitor\kb\mouse\webcam etc. Other shops I’d recommend looking at are PCCaseGear and Scorptec.
Edit: As above: Whirlpool is an excellent resource.
