sounds like you have defective ram on the card.....but does this happen when using either of the connectors? VGA as well as DVI?

If so, I would say bad ram, if not, and only the DVI, I would say the controller chip for the DVI has some errors.

anyways....seeing as how old the card is, I wouldn't put too much time into it.  those cards can be had for 5 euros or something

Did you take ESD-precautions (Electric Static Discharge) when handling the GeForce 4 Ti4200? RAM is quite sensitive!

Also check if your card is bent in any way. Sometimes I notice that slightly tilting a card when it's installed in it's AGP-slot will make the problems go away. If you try this method (on your own risk) tilt the card slightly before turning on your PC and keep it tilted when you turn it on. It's not really a fix but I used this trick to benchmark a few rare graphic cards that were damaged.

Unfortunately some cards simply die, even if you are very careful with them.

I recently tested a few cards that I wanted to sell, they were tested 1 or 2 years ago, they  worked perfectly then. I stored them in very good conditions, in antistatic bags, at constant room temperature, when I tested them again they were giving artifacts - small fots all over the screen

Just like ultima said, don't worry about it, it's a very common and cheap cards, be glad that it didn't happen to a V5 6000, a Quantum3D brick, etc...

Before you junk that card (if you're certain is it defective with such issues), there's a last ditch trick.

You can "bake" the hardware, if the suspected problem is a 'cold' solder point or unstable/broken electrical connection anywhere on the PCB to the ICs.

The methods and recommendations vary, but with plastic parts removed (=usually requires entire cooler to be removed) and exposed to ~125/max. 150deg Celsius for 60/30 minutes respectively, it is often possible to revive the hardware back to fully functional condition.

Most people reported very good results with simply placing the Video card i.e. onto a ceramic plate into a preheated conventional oven.
The surface should allow the card to rest on its entire surface to preclude any bending tendencies of the card (i.e. it shouldn't rest only on its edges).

While it sounds a bit crazy, the reason for that last ditch quickfix to actually work quite often is based on the metallurgic behaviour of the soldering compound used on the PCBs.
If any line developed a weak point with unstable or broken electrical connection, exposing the soldering compound to these temperatures for a limited time causes parts of the compound to re-organize sufficiently enough on a molecular level to close electrical connections again.

Of course, this method does nothing to defective chips itself, but the majority of aging video card issues seems to be broken/cold solder points/connections. These likely occur due to repeated exposure to the typical thermal stress after many years of use.

If attempted without success on first time (i.e. at relatively low temperature), a 2nd try with higher temperature usually does the trick. About 135 to max. 150deg Celsius for about 30 Minutes seems a sweet spot as far as I can tell.

The capacitors, ICs, VRMs and the PCB itself are typically able to temporarily accept exceeding their temperature design limits in unpowered condition.

It is important to note that the cooldown period should be very gentle (no attempt must be made to accelerate the cooling process), as this would induce unwanted very high thermal stress on the soldering points and defeat the purpose of the entire procedure.
Also, the extraction of the hardware should occur careful and free of any mechanical shocks while it is still at temperature.

If the procedure has no effect even after two attempts and the hardware i.e. has RAM chips or other important ICs also soldered on its backside, repeating the procedure with the card upside down can help (this practically reverses the direction of gravity on the PCB, in which the soldering compound can partly reorganize).

So far I've only revived an USB device with that method, but that went from 100% non-working back to fully working and I have it in operation ever since.

PS.
Speaking of capacitors :
The 2nd most common reason for older Video card failures are broken/blown/leaking capacitors. These have a limited lifespan defined by a time/temperature curve and will eventually fail. Sometimes visibly (cracked tops), sometimes one can only smell the electrolytes that have leaked.
Newer cards use modern high quality hardcap capacitors designed for 125deg. or higher with drastically improved lifespans.

AFAIK the oven trick can work more likely as a temporary fix instead of a permanent solution. The many hardware stories that I read tell that soon or later the soldering issues could back at any time.

BTW, if theren't other choices first to trash the hardware, this could be a funny way to go.

Just got another card from the same place with a similar issue, only that the distortions and artifacts are much worse in VGA.  The card is an Radeon X1600 Pro AGP 512mb.  With both cards when I used the DVI, I got no signal at all.  Nothing,  Is there something I need to do to enable DVI?  If only the vga is affected perhaps the card might work in DVI?  Maybe not, but it's worth a shot, right? 

I should also say that the card I use now is not AGP PRo.  It's anothe AGP type.