You can easily find recievers that have built in DVD/CD Changers... but as for the tape deck... more than likely that'd have to be a seperate component. The recievers with built in CD/DVD Changers are usually referred to as "Home-Theater-In-A-Box", and if quality is anything you're concerned with I'd recommend staying away from such a unit (we have one in our living room and it works well, it's just for the same price I could have gotten something quite a bit better).
I'd encourage you to get a seperate reciever, seperate CD/DVD Changer, and seperate tape deck. The only units that have all three as one would be your bookshelf systems. Just do some research on the components. You could pair something together for quite cheap:
Not the best reciever out there, but it'd do the trick. $69.95
Sony 5-Disc CD/DVD Changer
w/ 1080i up-conversion. Again, not the best but it'd work for what you're after. $109.95
And finally the cassette deck. This will be the most expensive unit, probably due to them being more rare. Anyhow, take your pick.
I'd go for the one that'll convert the cassette to MP3 for your PC.
Altogether you're looking at right about $330.00 for a complete new setup that'd smoke any pc-speakers while adding greater functionality (5-disc CD/DVD changer and dual cassette deck). Then, when you have the cash, replace those surround speakers with some proper bookshelf speakers- like these.
You'd then have a rockin' setup.
And if ever needed, replace you're current center speaker with something along the lines of this.
Again, none of this is top-of-the-line equipment. There's definitely significantly better components out there... but it'd work for what you're after.