The first link clicked is this one:
http://www.labor.maryland.gov/employment/uibenefits.shtml
That page opens with http instead of https and when you try https it has a security certificate issue. It‘s pointing to: www.dllr.state.md.us

When going directly to the last link it works without security issue:
https://employer.beacon.labor.md.gov/

I noticed that reference opening with http instead of https. Ironically, I don't have issues with any PC outside their network. She tried to do this from an XP PC that's on the network using Internet Explorer and experienced the same failure.
So now my thought is that it's an internal Internet access issue versus just the PC itself. In other words, there is a Windows 10 workstation and an XP workstation (the XP PC has a specific database that only works on XP)
- their network isn't anything fancy. It's just a basic Comcast modem Gateway and two computers
I was trying to troubleshoot remotely via remote connection
- I reset the DNS on this PC to use IP addresses 8.8.8.8 and 8.8.4.4 - to route accessing the Internet outside of Comcast DNS default DNS servers
perform the following with an elevated command prompt.
ipconfig /flushdns
ipconfig /registerdns
ipconfig /release
ipconfig /renew
while I attempted to do the IP config release, I got disconnected as expected but the PC didn't respond to renewing and would not let me reconnect. I will revisit the issue tomorrow when the user comes in to the office in the morning

Based on your reply, I wasn't sure whether you had any issues connecting to that link.
I didn't have any issues on my Windows 10 PC

I noticed that the page opened with http instead of https -
- when I do this for my computer it does state that it's not secure. is that what you're seeing?
as I mentioned above, I might have in any issues connecting to any link on that site. it sounds like you not having any issues either

https://employer.beacon.labor.md.gov/ 
- I can't recall if I actually tried https://employer.beacon.labor.md.gov/  - I know that I tried employer.beacon.labor.md.gov/  and employer.beacon.labor.md.gov/  (with and without the / )
I don't think that I tried https://employer.beacon.labor.md.gov/ from her PC but I will

Thanks for your input so far

we attempted again this morning when the user came in to no avail
I will plan going on site and try to access the site from my laptop to see if it fails on site behind their Verizon Fios router.
I can access the site from my office and from my laptop with no problem. I'll keep you posted

I was trying the URL’s from an iPad in both Safari and Brave browsers. Using a VPN to get access because .gov sites apparently don’t service requests outside US. I’m using Open DNS but resolving isn’t the issue - the certficate is I think. You can verify the certificate using fe digicert: https://www.digicert.com/help/ Possibly the user has some sort of protection installed against cert issues.

I was able to make this work for my laptop at my home office. But it failed on site which tells me there is a networking related issue that I need to resolve.

I appreciate very much your input