MIXED MODEL WITH REPEATED MEASURES

I am trying to specify a mixed model for my research, but I can't 
quite get it to work. I've spent several weeks looking thru various 
online sources to no avail. I can't find an example of someone trying 
to do precisely what I'm trying to do. I'm hoping some smart member of 
this mailing list may be able to help.

First off, full disclosure: (1) I'm an engineer by trade, so the 
problem may be related to my ignorance of statistics, and/or (2) I'm 
fairly new to R, so the problem may be related to my ignorance of R 
syntax. Here is the basic structure of my data (in longitudinal form):

The rows below each subject are repeated measures (in years), with the 
specific pattern of repeated measurements unique to each subject. The 
data contains fixed effects and random effects, and there is clearly 
correlation in the random effects within each subject. The DepVar 
column represents the dependent variable which is a constant for each 
subject. All the data is empirical, but I wish to create a predictive 
model. Specifically, I wish to predict the value for DepVar for new

So I understand enough about statistics to know that I must employ a 
mixed model. I further understand that I must specify a covariance 
matrix structure. Given the relatively high degree of correlation in 
consecutive years, an AR(1) structure seems like a good starting 
point. I have been trying to build the model in SPSS, but without 
success, so I've recently turned to R. My first attempt was as 
follows--

ModelFit <- lme(fixed = DepVar ~FixedVar1+FixedVar2, random =
~RandomVar1+RandomVar2 | Subject, na.action = na.omit, data = dataset, 
corr = corAR1())

I assume this can't be the right specification since it neglects the 
repeated measure aspect of the data, so I instead decided to employ 
the
corCAR1 structure, i.e.--

ModelFit <- lme(fixed = DepVar ~FixedVar1+FixedVar2, random =
~RandomVar1+RandomVar2 | Subject, na.action = na.omit, data = dataset, 
corr = corCAR1(0.5, form = ~ Years | Subject))

Now perhaps neither correlation structure is the right one (probably a 
different discussion for another day), but the problem I'm 
experiencing seems to occur regardless of the structure I specify. In 
both cases, I get the following error--

Error in solve.default(estimates[dimE[1] - (p:1), dimE[2] - (p:1), 
drop =
FALSE]) : 

  system is computationally singular: reciprocal condition number =
5.42597e-022

Anybody know what is going wrong here? This error appears to be 
related to the fact that the DepVar is constant for each subject, 
because when I select a different dependent variable that is different 
for each repeated measure w/in the subject, I do not get this error.