Many of the off-brand DVD players can be made region free. Google the model number. Also, look for a button on the remote marked P/N or N/P.

The friends who advise me about this stuff have never mentioned the issues you describe.
Perhaps you should learn a lesson from that. You made the unsolicited post to me. I don't hold your friends responsible for what you don't know. When it's your reputation at stake, it would be wise to do the hard work of knowing our business yourself. IJS
Live long and prosper

Oh yes, VLC is great! I use it a lot, and contribute money to its development regularly. Soyou're welcome!
However it's not the software on the computer that keeps track of the region setting, it's the firmware in the DVD drive itself. Play media with different region on drives with RPC-2 firmware something like 5 times and the drive itself refuses to play any video DVD except from the last region you used. There are ways around this, but it's a pain. Even more so with new computers with UEFI instead of BIOS. Thanks to Microsoft's stranglehold on the market, a locked-down UEFI can also block firmware updates to drives.

If you're in the USA, your TV probably won't be able to process a direct 50hz PAL signal. Your best bet would be to have a dedicated DVD-rom drive in your computer set to Region 2, that will be able to convert the signal for input into your TV.

That's probably the most straightforward way to go. Good luck!

Thank you for your response. I have already decided to look into a region-free DVD player.

Chances are that your old DVD player will not do the job.
Since your computer is relatively new, and (at least on the high end) the progress of computer "power" has leveled off in recent years, you should have good results playing your Region 2 DVDs on it. You may need to get special "region free" software to play it, and reset the region of your DVD drive in Device Manager in Windows. Computer DVD drives will lock to one region after a certain number of times, so switch
very
judiciously.
If you're comfortable using your computer to watch Region 2 discs, you might want to invest in an external USB DVD drive to use as your permanent Region 2 drive. Likewise, you could buy a "region free" DVD player if you prefer to use a TV. In general, the cheapest, no-name model will often serve your purposes as well or better than big name players. Either way, your cost should be much less than $50US for the hardware.